AMENDMENT NO. 1 TO SECOND AMENDED AND RESTATED LIMITED LIABILITY COMPANY AGREEMENT OF LINN ENERGY, LLC

Exhibit 4.1

     Execution Copy

AMENDMENT NO. 1 TO SECOND AMENDED AND RESTATED
LIMITED LIABILITY COMPANY AGREEMENT OF
LINN ENERGY, LLC

     THIS AMENDMENT NO. 1 TO SECOND AMENDED AND RESTATED LIMITED LIABILITY COMPANY AGREEMENT OF LINN ENERGY, LLC (this “Amendment”), dated as of October 24, 2006, is entered into and effectuated by the Board of Directors (the “Board”) of Linn Energy, LLC, a Delaware limited liability company (the “Company”), pursuant to authority granted to it in Sections 5.5 and 11.1 of the Second Amended and Restated Limited Liability Company Agreement of the Company, dated as of January 19, 2006 (the “Limited Liability Company Agreement”). Capitalized terms used but not defined herein are used as defined in the Limited Liability Company Agreement.

     WHEREAS, Section 5.5(a) of the Limited Liability Company Agreement provides that the Company may issue additional Company Securities for any Company purpose at any time and from time to time for such consideration and on such terms and conditions as the Board shall determine, all without the approval of any Members;

     WHEREAS, Section 5.5(b) of the Limited Liability Company Agreement provides that the Company Securities authorized to be issued by the Company pursuant to Section 5.5(a) of the Limited Liability Company Agreement may be issued in one or more classes, or one or more series of any such classes, with such designations, preferences, rights, powers and duties (which may be senior to existing classes and series of Company Securities) as shall be fixed by the Board;

     WHEREAS, Section 11.1(c)(vii) of the Limited Liability Company Agreement provides that the Board, without the approval of any Member (subject to the provisions of Section 5.6 of the Limited Liability Company Agreement), may amend any provision of the Limited Liability Company Agreement that the Board determines to be necessary or appropriate in connection with the authorization of issuance of any class or series of Company Securities pursuant to Section 5.5 of the Limited Liability Company Agreement, and the Board has determined that the amendments contemplated hereby are necessary or appropriate in connection therewith;

     WHEREAS, the Board has determined that the issuance of the Class B Units provided for in this Amendment is permitted by Section 5.6 of the Limited Liability Company Agreement;

     WHEREAS, Section 11.1(c)(iv) of the Limited Liability Company Agreement provides that the Board, without the approval of any Member, may amend any provision of the Limited Liability Company Agreement to reflect a change that the Board determines does not adversely affect the Members (including any particular class of Interests as compared to other classes of Interests) in any material respect, and the Board has determined that such amendments contemplated hereby do not adversely affect the Members in any material respect; and

     WHEREAS, the Board deems it in the best interest of the Company to effect this Amendment to provide for (i) the issuance of the Class B Units, (ii) the conversion of the Class B Units into Units in accordance with the terms described herein and (iii) such other matters as are provided herein.

     NOW, THEREFORE, it is hereby agreed as follows:

     A. Amendment. The Limited Liability Company Agreement is hereby amended as follows:

     1. Section 1.1 of the Limited Liability Company Agreement is hereby amended to add or amend and restate the following definitions in the appropriate alphabetical order:

     “Capital Account True-Up Election” has the meaning set forth in Section 6.1(d)(xii)(C).

     “Class B Unit” means a Company Security representing a fractional part of the Interests of all Members, and having the rights and obligations specified with respect to the Class B Units in this Agreement. A “Class B Unit” shall not constitute a Unit until such time as such Class B Unit is converted into a Unit pursuant to Section 5.10.

     “Issue Price” means the price at which a Unit or Class B Unit is purchased from the Company, net of any sales commissions or underwriting discount charged to the Company; for the avoidance of doubt, in the case of the Class B Units, the Issue Price shall be deemed to be $20.55 per Class B Unit and, in the case of the Privately Placed Units, $21.00 per Privately Placed Unit.

     “Percentage Interest” means, as of any date of determination (a) as to any Unitholder or holder of Class B Units holding Units or Class B Units, the product obtained by multiplying (i) 100% less the percentage established pursuant to clause (b) below by (ii) the quotient obtained by dividing (A) the number of Units and Class B Units held by such Unitholder or holder of Class B Units by (B) the total number of all Outstanding Units or Outstanding Class B Units and (b) as to the holders of other Company Securities issued by the Company in accordance with Section 5.5, the percentage established as part of such issuance.

     “Per Unit Capital Amount” means, as of any date of determination, the Capital Account, stated on a per Unit, Class B Unit or Privately Placed Unit basis, as the case may be, underlying any Unit, Class B Unit or Privately Placed Unit, as the case may be, held by a Person.

     “Private Placement Value” means with respect to the Class B Units $22.27 per Class B Unit and the Privately Placed Units $22.27 per Privately Placed Unit.

     “Privately Placed Units” means the Units issued pursuant to the Unit Purchase Agreement.

     “Pro Rata” means (a) when modifying Units, Class B Units, Privately Placed Units or any class of any thereof, apportioned equally among all designated Units, Class B Units or

Privately Placed Units, as the case may be, in accordance with their relative Percentage Interests, and (b) when modifying Members, apportioned among all designated Members in accordance with their relative Percentage Interest.

     “Remaining Net Positive Adjustments” means, as of the end of any taxable period, with respect to the holders of Units, Privately Placed Units or Class B Units, the excess of (i) the Net Positive Adjustments of the holders of Units, Privately Placed Units or Class B Units as of the end of such period over (ii) the sum of those Members’ Share of Additional Book Basis Derivative Items for each prior taxable period.

     “Share of Additional Book Basis Derivative Items” means, in connection with any allocation of Additional Book Basis Derivative Items for any taxable period, with respect to the holders of Units, Privately Placed Units or Class B Units, the amount that bears the same ratio to such Additional Book Basis Derivative Items as the holders’ Remaining Net Positive Adjustments as of the end of such period bears to the Aggregate Remaining Net Positive Adjustments as of that time.

     “Unit” means a Company Security representing a fractional part of the Interests of all Members, and having the rights and obligations specified with respect to Units in this Agreement, which includes Privately Placed Units. The term “Unit” does not refer to a Class B Unit prior to its conversion into a Unit pursuant to the terms hereof.

     “Unit Majority” means a majority of the Outstanding Units.

     “Unit Purchase Agreement” means the Class B Unit and Unit Purchase Agreement dated as of October 24, 2006 between the Company and the purchasers named therein.

     2. Article IV of the Limited Liability Company Agreement is hereby amended to add a new Section 4.6(c) as follows:

     (c) The transfer of a Class B Unit or a Privately Placed Unit shall be subject to the restrictions imposed by Section 6.5.

     3. Section 5.4(a) of the Limited Liability Company Agreement is hereby amended to add the following at the end of such section:

     The initial Capital Account balance in respect of each Class B Unit shall be the Private Placement Value for such Class B Unit, and the initial Capital Account balance of each holder of Class B Units in respect of all Class B Units held shall be the product of such initial balance for a Class B Unit multiplied by the number

of Class B Units held thereby. The initial Capital Account balance in respect of each Privately Placed Unit shall be the Private Placement Value for such Privately Placed Unit, and the initial Capital Account balance of each holder of Privately Placed Units in respect of all Privately Placed Units held shall be the product of such initial balance for a Privately Placed Unit multiplied by the number of Privately Placed Units held thereby. Immediately following the creation of a Capital Account balance in respect of each Class B Unit, each holder acquiring a Class B Unit at original issuance shall be deemed to have received a cash distribution in respect of such Class B Units in an amount equal to the product of (x) the total number of Class B Units so acquired by such holder multiplied by (y) the difference between the Private Placement Value and the Issue Price of a Class B Unit. Immediately following the creation of a Capital Account balance in respect of each Privately Placed Unit, each Unitholder acquiring a Privately Placed Unit at original issuance shall be deemed to have received a cash distribution in respect of such Privately Placed Units in an amount equal to the product of (x) the total number of Privately Placed Units so acquired by such Unitholder multiplied by (y) the difference between the Private Placement Value and the Issue Price of a Privately Placed Unit. The purpose of the four preceding sentences is to provide the initial purchasers of Class B Units and Privately Placed Units with a net Capital Account in the Class B Units and Privately Placed Units on the date of purchase equal to the Issue Price paid by those purchasers for the Class B Units and Privately Placed Units.

     4. Section 5.4(c)(i) of the Limited Liability Company Agreement is hereby amended to add the following at the end of such section:

     Any adjustments that are made under this paragraph in connection with the issuance of the Class B Units or the Privately Placed Units shall be based on the Private Placement Value of the Class B Units and the Privately Placed Units.

     5. Article V of the Limited Liability Company Agreement is hereby amended to add a new Section 5.10 creating a new series of Company Securities as follows:

     Section 5.10 Establishment of Class B Units.

     (a) General. The Board hereby designates and creates a series of Company Securities to be designated as “Class B Units” and consisting of a total of 9,185,965 Class B Units, and fixes the designations, preferences and relative, participating, optional or other special rights, powers and duties of holders of the Class B Units as set forth in this Section 5.10.

     (b) Allocations. Except as otherwise provided in this Agreement, including Section 6.1(d)(iii), all items of Company income, gain, loss, deduction and credit shall be allocated to the Class B Units to the same extent as such items would be so

allocated if such Class B Units were Units (other than Privately Placed Units) that were then Outstanding.

     (c) Distributions. Each Class B Unit shall have the right to share in Company distributions on a Pro Rata basis with the Units, with the amount of distributions on each such Class B Unit being equal to 115% of the quarterly cash distribution amount payable on each Unit.

     (d) Vote of Unitholders. Except as provided in this Section 5.10, the Class B Units are not convertible into Units. The Board shall, as promptly as practicable following the issuance of the Class B Units, but in any event not later than 90 days from the issuance of the Class B Units, take such actions as may be necessary or appropriate to submit to a vote or consent of the holders of the Units the approval of a change in the terms of the Class B Units to provide that each Class B Unit will automatically convert into one Unit (subject to appropriate adjustment in the event of any split-up, combination or similar event affecting the Units that occurs prior to the conversion of the Class B Units) effective immediately upon such approval by the Unitholders of the issuance of additional Units upon such automatic conversion without any further action by the holders thereof. The vote or consent required for such approval will be the requisite vote required under this Agreement and under the rules or staff interpretations of the National Securities Exchange on which the Units are listed or admitted to trading for the listing or admission to trading of the Units that would be issued upon any such conversion. Upon receipt of such approval and compliance with Section 5.10(f), the terms of the Class B Units will be changed, automatically and without further action, so that each Class B Unit is converted into one Unit and, immediately thereafter, none of the Class B Units shall be Outstanding.

     (e) Change in Rules of National Securities Exchange. If at any time (i) the rules of the National Securities Exchange on which the Units are listed or admitted to trading or the staff interpretations of such rules are changed or (ii) facts or circumstances arise so that no vote or consent of Unitholders is required as a condition to the listing or admission to trading of the Units that would be issued upon any conversion of any Class B Units into Units as provided in Section 5.10(d), the terms of such Class B Units will be changed so that each Class B Unit is converted (without further action or any vote of any Unitholders other than compliance with Section 5.10(f)) into one Unit (subject to appropriate adjustment in the event of any split-up, combination or similar event affecting the Units that occurs prior to the

conversion of the Class B Units) and, immediately thereafter, none of the Class B Units shall be Outstanding.

     (f) Surrender of Certificates. Upon receipt of the approval of the holders of the Units to convert the Class B Units into Units in accordance with Section 5.10(d) or a change in rules of the National Securities Exchange or a change in facts and circumstances as described in Section 5.10(e), the Board shall give the holders of the Class B Units prompt notice of such approval or change and, subject to Section 6.5, each holder of Class B Units shall promptly surrender the Class B Unit Certificates therefor, duly endorsed, at the office of the Company or of any transfer agent for the Class B Units. In the case of any such conversion, the Company shall, as soon as practicable thereafter, issue and deliver at such office to such holder of Class B Units one or more Unit Certificates, registered in the name of such holder, for the number of Units to which such holder shall be entitled as aforesaid. Such conversion shall be deemed to have been made as of the date of the event specified in Section 5.10(d) or Section 5.10(e), as the case may be, and the Person entitled to receive the Units issuable upon such conversion shall be treated for all purposes as the record holder of such Units on said date.

     (g) Voting Rights. The Class B Units are non-voting, except that the Class B Units shall be entitled to vote as a separate class on any matter that adversely affects the rights or preferences of the Class B Units in relation to other classes of Interests (including as a result of a merger or consolidation) or as required by law. The approval of a majority of the Class B Units shall be required to approve any matter for which the holders of the Class B Units are entitled to vote.

     6. Section 6.1(c) of the Limited Liability Company Agreement is hereby amended to restate Section 6.1(c)(i)(B) as follows:

     (B) Second, 100% to all Unitholders and holders of Class B Units in accordance with their respective Percentage Interests.

     7. Section 6.1(c) of the Limited Liability Company Agreement is hereby amended to add a new Section 6.1(c)(ii)(A) as follows:

     (A) First, to the holders of Class B Units, Pro Rata, until the Capital Account in respect to each Class B Unit then Outstanding has been reduced to zero; and

     8. Section 6.1(c)(ii)(A) of the Limited Liability Company Agreement is hereby redesignated as Section 6.1(c)(ii)(B), and Section 6.1(c)(ii)(B) of the Limited Liability Company Agreement is hereby redesignated as Section 6.1(c)(ii)(C).

     9. Article VI of the Limited Liability Company Agreement is hereby amended to add a new Section 6.1(d)(iii) as follows:

     (iii) Priority Allocations. If the amount of cash or the Net Agreed Value of any property distributed (except cash or property distributed or deemed distributed pursuant to Section 5.4(a) of this Agreement with respect to Class B Units or Privately Placed Units, or Section 10.3 of this Agreement) to any holder of Class B Units with respect to its Class B Units for a taxable year is greater (on a per Class B Unit basis) than the amount of cash or the Net Agreed Value of property distributed to the Unitholders with respect to their Units (on a per Unit basis), then each holder of Class B Units receiving such greater cash or property distribution shall be allocated gross income in an amount equal to the product of (a) the amount by which the distribution (on a per Class B Unit basis) to such holder of Class B Units exceeds the distribution (on a per Unit basis) to the Unitholders and (b) the number of Class B Units owned by the holder of Class B Units.

     10. Article VI of the Limited Liability Company Agreement is hereby amended to add a new Section 6.1(d)(xii) as follows:

     (xii) Allocations for Class B Units and Privately Placed Units.

     (A) With respect to any taxable period of the Company ending upon, or after, a Book-Up Event, a Book-Down Event or a sale of all or substantially all of the assets of the Company occurring after the date of issuance of the Class B Units and the Privately Placed Units, Company items of income or gain for such taxable period shall be allocated 100% (1) to the Members holding Class B Units or converted Class B Units that are Outstanding as of the time of such event in proportion to the number of Class B Units or converted Class B Units held by such Members, until each such Member has been allocated the amount that increases the Capital Account of such Class B Unit or converted Class B Unit to the Per Unit Capital Amount for a then outstanding Unit (other than a converted Class B Unit or a Privately Placed Unit) and (2) to the Members holding Privately Placed Units that are Outstanding as of the time of such event in proportion to the number of Privately Placed Units held by such Members, until each such Member has been allocated the amount that increases the Capital Account of such Privately Placed Unit to the Per Unit Capital Amount for a then outstanding Unit (other than a Privately Placed Unit or a Class B Unit).

     (B) With respect to any taxable period of the Company ending upon, or after, the transfer of converted Class B Units or Privately Placed Units to a Person that is not an Affiliate of the holder, Company items of income or gain for such taxable period shall be allocated 100% (1) to the

Members transferring such converted Class B Units in proportion to the number of converted Class B Units transferred by such Members, until each such Member has been allocated the amount that increases the Capital Account of such converted Class B Unit to the Per Unit Capital Amount for a then outstanding Unit (other than a converted Class B Unit or a Privately Placed Unit) and (2) to the Members transferring such Privately Placed Units in proportion to the number of Privately Placed Units transferred by such Members, until each such Member has been allocated the amount that increases the Capital Account of such Privately Placed Unit to the Per Unit Capital Amount for a then outstanding Unit (other than a Privately Placed Unit or a converted Class B Unit).

     (C) With respect to the first taxable period of the Company ending upon, or after, the date of issuance of the Class B Units or the Privately Placed Units, at the election of a Member holding Class B Units or Privately Placed Units (the “Capital Account True-Up Election”), items of income or gain for such taxable period shall be allocated 100% to the Members making such Capital Account True-Up Election with respect to Class B Units or Privately Placed Units that are Outstanding as of the time of such Capital Account True-Up Election in proportion to the number of Class B Units or Privately Placed Units held by such Members, until each such Member has been allocated the amount that increases, the Capital Account of such Class B Unit or Privately Placed Unit to the Per Unit Capital Amount for a then outstanding Unit (other than a Class B Unit or a Privately Placed Unit).

     11. Section 6.1(d)(xi)(A) of the Limited Liability Company Agreement is hereby amended to replace the phrase “this Amended and Restated Limited Liability Company Agreement” in the two places that it appears to “this Agreement”.

     12. Section 6.4 of the Limited Liability Company Agreement is hereby amended to replace the reference to “Section 5.6(b)” with “Section 5.5(b)”.

     13. Article VI is hereby amended to add a new Section 6.5 as follows:

     Section 6.5 Special Provisions Relating to Holders of Class B Units and Privately Placed Units. A holder of (1) a Privately Placed Unit or (2) a Class B Unit that has converted into a Unit pursuant to Section 5.10 shall be required to provide notice to the Board of the number of Privately Placed Units or converted Class B Units transferred by such holder no later than the last Business Day of the calendar year during which such transfer occurred, unless (x) the transfer is to an Affiliate of the holder or (y) by virtue of the application of Section 6.1(d)(xii)(B) to a prior transfer of the Unit or the application of Section 6.1(d)(xii)(A) or Section 6.1(d)(xii)(C), the Board has previously determined, based on advice of counsel, that the Privately Placed Unit or converted Class B Unit should have, as a substantive matter, like intrinsic economic and federal income tax characteristics of an Initial Unit; provided, that such holder may cure any failure to provide such notice by providing such notice within 20 days of the last Business Day of

such calendar year. The sole and exclusive remedy for any holder’s failure to provide any such notice shall be the enforcement of the remedy of specific performance against such holder and there will be no monetary damages. In connection with the condition imposed by this Section 6.5, the Board shall take whatever steps are required to provide economic uniformity to the Privately Placed Units and converted Class B Units in preparation for a transfer thereof, including the application of Section 6.1(d)(xii)(B); provided, however, that no such steps may be taken that would have a material adverse effect on the Unitholders holding Units represented by Unit Certificates.

     B. Agreement in Effect. Except as hereby amended, the Limited Liability Company Agreement shall remain in full force and effect.

     C. Applicable Law. This Amendment shall be construed in accordance with and governed by the laws of the State of Delaware, without regard to principles of conflicts of laws.

     D. Invalidity of Provisions. If any provision of this Amendment is or becomes invalid, illegal or unenforceable in any respect, the validity, legality and enforceability of the remaining provisions contained herein shall not be affected thereby.

     IN WITNESS WHEREOF, this Amendment has been executed as of the date first written above.