RHYTHM PHARMACEUTICALS, INC. Performance Unit Agreement

Exhibit 10.4

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RHYTHM PHARMACEUTICALS, INC.

2017 EQUITY INCENTIVE PLAN

Performance Unit Agreement

This Performance Unit Agreement (this “Agreement”), dated as of [ ● ] (the “Date of Grant”), is between Rhythm Pharmaceuticals, Inc., a corporation organized under the laws of the State of Delaware (the “Company”) and [ ● ] (the “Participant”).  Capitalized terms used in this Agreement without definition shall have the respective meaning ascribed to such capitalized terms in the Rhythm Pharmaceuticals, Inc. 2017 Equity Incentive Plan (as the same may be amended from time to time, the “Plan”).

1.Grant of Performance Units.  Subject to the terms and conditions set forth in this Agreement and in the Plan, the Company hereby grants the Participant [ ● ] Performance Units, subject to the restrictions set forth below and in the Plan (the “Stock Units”).  The Stock Units shall be eligible to be earned based on the Company’s achievement of the performance milestones set forth on Appendix A hereto during the Performance Period (as defined on Appendix A).  Each Stock Unit represents the right of the Participant to receive a number of shares of common stock of the Company (“Stock”) as determined in accordance with Appendix A hereto, an equivalent amount of cash based on the value of a share of Stock, or any combination of the foregoing, as determined by the Committee, if and when the specified conditions are met in Section 3 below, and on the applicable settlement date set forth in Section 5 below.

▇.▇▇ Rights Prior to Settlement.  Stock Units represent hypothetical shares of Stock, and not actual shares of Stock.  No shares of Stock shall be issued to the Participant at the time the grant of the Stock Units is made, and the Participant shall not be, and shall not have any of the rights or privileges of, a stockholder of the Company with respect to any Stock Units.  The Participant shall not have any interest in any fund or specific assets of the Company by reason of this award.

3.Vesting.

a)As of the date of this Agreement, all of the Stock Units shall be unvested and subject to a Risk of Forfeiture pursuant to Section 4 below.

b)Subject to the terms of this Section 3, the Stock Units shall vest in a single installment on the date that the Committee determines the Total Achievement Percentage (as defined in Appendix A hereto) for the Performance Period, provided that the Participant continues his or her employment or other association with the Company or one of its Affiliates from the Date of Grant until such vesting date (the “Vesting Date”).

c)In the event a Change of Control occurs before the Vesting Date, 100% of the Stock Units that have not terminated under Section 4 (or, to the extent the Committee determines sufficient milestones set forth on Appendix A have been attained, or if the Committee elects in its discretion to determine that it is probable such milestones will be attained, in either case, so as to result in more than 100% of the Stock Units that have not been terminated being scheduled to vest on the Vesting Date, such larger number of Stock Units as so determined by the Committee) will vest upon the occurrence of the Change of Control, and the Committee may take

such actions as it deems appropriate pursuant to the Plan.  This Section 3(c) shall be applied to the Stock Units regardless of and shall supersede any Change of Control vesting terms (including any “double trigger” vesting terms) provided in an employment agreement, offer letter, severance agreement or other contract entered into by and between the Participant and the Company or an Affiliate (in any case, an “Employment Agreement”), except that to the extent such Employment Agreement provides for the Participant to remain eligible to vest in the Stock Units upon a Change in Control that occurs during a period of up to three months following termination of the Participant’s employment, the Participant shall remain eligible to vest in Stock Units under this Section 3(c) during such period, subject to any terms or conditions of the Employment Agreement that apply to such Change in Control vesting (including any requirement to timely execute and not revoke a release of claims).

d)Those Stock Units that vest pursuant to this Section 3 or pursuant to any action taken by the Committee pursuant to the Plan shall become free from the termination provisions pursuant to Section 4 below.

4.Termination of Stock Units.  If the Participant ceases employment or other association with the Company and its Affiliates for any reason before all of the Stock Units vest, any unvested Stock Units shall automatically terminate and shall be forfeited as of the date of the Participant’s termination of employment or other association, unless otherwise provided under Section 3(c) or determined by the Committee.  In addition, in the event that the Committee determines that any of the milestones set forth on Exhibit A has not or cannot be achieved during the Performance Period (including at a target or maximum level, as applicable) a number of Stock Units equal to the total number of Stock Units multiplied by the applicable Achievement Percentage for such milestone shall automatically terminate. No settlement or payment shall be made with respect to any Stock Units that terminate as described in this Section 4 or on Appendix A.

5.Settlement of Stock Units and Tax Withholding.

a)If the Stock Units vest in accordance with the provisions of Appendix A and Section 3 above, then, subject to the provisions of this Section 5(a) and Sections 5(b), 5(c) and 12 below, the Company shall issue to the Participant a number of shares equal to (i) the Total Achievement Percentage for the Performance Period multiplied by the total number of Stock Units or (ii) in the event Stock Units vest under Section 3(c), such other number of shares as corresponds to the number of Stock Units vesting under such Section, in any case, rounded down to the nearest whole share, or an equivalent amount of cash based on the value of a share of Stock, or a combination of the foregoing, as determined by the Committee, subject to applicable tax withholding obligations, as soon as reasonably practicable after the Vesting Date applicable to such vested Stock Unit.  Notwithstanding anything express or implied in the foregoing provisions of this Section 5(a) to the contrary, in no event shall settlement of a vested Stock Unit occur later than the fifteenth day of the third calendar month following the calendar year in which the Vesting Date applicable to such vested Stock Unit occurs, and in no event shall Participant be permitted, directly or indirectly, to designate the calendar year of payment.

b)All obligations of the Company under this Agreement shall be subject to the right of the Company as set forth in the Plan to collect applicable federal, state, local, foreign or

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other withholding taxes if, when, and to the extent required by law prior to the issuance of shares of Stock or payment in cash.  The Company shall satisfy any applicable withholding requirement with respect to the issuance of shares of Stock from proceeds of a sale of a portion of the shares of Stock effected by the Company’s designated broker; the Participant’s acceptance of the Stock Units shall constitute the Participant’s authorization to the broker to effect such sale as promptly as practicable.  In the event payment is to be made in a form other than shares of Stock, then the Company shall collect from the Participant the applicable withholding taxes pursuant to such procedures as the Company deems appropriate under the circumstances.

c)The obligation of the Company to deliver Stock shall also be subject to the condition that if at any time the Board shall determine in its discretion that the listing, registration or qualification of any shares of Stock upon any securities exchange or under any state or federal law, or the consent or approval of any governmental regulatory body is necessary or desirable as a condition of, or in connection with, the issuance of such shares, such shares may not be issued in whole or in part unless such listing, registration, qualification, consent or approval shall have been effected or obtained free of any conditions not acceptable to the Board.  The issuance of shares of Stock, if any, to the Participant pursuant to this Agreement is subject to any applicable laws or regulations of the United States or of any state, municipality or other country having jurisdiction thereof.

▇.▇▇ Stockholder Rights.  Neither the Participant, nor any person entitled to receive Stock Units in the event of the Participant’s death, shall have any of the rights and privileges of a stockholder with respect to shares of Stock, including voting or dividend rights, until such shares of Stock have been issued upon settlement of Stock Units.  The Participant acknowledges that no election under Section 83(b) of the Code is available with respect to Stock Units.

7.Grant Subject to Plan Provisions.  This grant is made pursuant to the Plan, the terms of which are incorporated herein by reference, and in all respects shall be interpreted in accordance with the Plan.  The grant and settlement of the Stock Units are subject to the provisions of the Plan and to interpretations, regulations and determinations concerning the Plan established from time to time by the Committee in accordance with the provisions of the Plan, including, but not limited to, provisions pertaining to (a) rights and obligations with respect to withholding taxes, (b) the registration, qualification or listing of the shares of Stock, (c) changes in capitalization of the Company and (d) other requirements of applicable law.  The Committee shall have the authority to interpret and construe the Stock Units pursuant to the terms of the Plan, and its decisions shall be conclusive as to any questions arising hereunder.

▇.▇▇ Employment or Other Rights.  The grant of the Stock Units shall not confer upon the Participant any right to be retained by or in the employ or service of the Company or any Affiliate and shall not interfere in any way with the right of the Company or any Affiliate to terminate the Participant’s employment or other association with the Company and its Affiliates.  The right of the Company and any Affiliate to terminate at will the Participant’s employment or other association at any time for any reason is specifically reserved.

9.Assignment and Transfers.  The Stock Units are not transferable, and shall not be sold, transferred, pledged, assigned, or otherwise alienated or hypothecated, other than by will or

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by the laws of descent and distribution.  This Agreement may be assigned by the Company without the Participant’s consent.

10.Governing Law; Counterparts.  This Agreement shall be construed and enforced in accordance with the laws of the State of Delaware, without regard to the conflict of laws principles thereof.  This Agreement may be executed in one or more counterparts all of which together shall constitute but one instrument.  In making proof of this Agreement it shall not be necessary to produce or account for more than one such counterpart.

11.Notice.  Any notice to the Company provided for in this instrument shall be addressed to the Company, at the Company’s principal place of business, addressed to the attention of the Company’s Treasurer, and any notice to the Participant shall be addressed to such Participant at his or her residence address last filed with the Company.  Any notice shall be delivered in accordance with Section 18 of the Plan.

12.Application of Section 409A of the Code.  This Agreement is intended to be exempt from or otherwise comply with the provisions of Section 409A of the Code.  Notwithstanding the foregoing, if any Stock Units constitute “deferred compensation” under Section 409A of the Code and such Stock Units become vested upon the Participant’s termination of employment (or other association), settlement of such vested Stock Units shall be delayed for a period of six (6) months after the Participant’s termination of employment (or other association) if the Participant is a “specified employee” as defined under Section 409A of the Code and if required pursuant to Section 409A of the Code.  If settlement of any Stock Units is delayed in accordance with the foregoing provisions of this Section 12, such Stock Units shall be settled and paid within thirty (30) days after the date that is six (6) months following the Participant’s termination of employment (or other association).  To the extent subject to Section 409A of the Code, settlement of the Stock Units may only be made in a manner and upon an event permitted by Section 409A of the Code, and each settlement of the Stock Units shall be treated as a separate payment, and the right to a series of installment payments under the Stock Units shall be treated as a right to a series of separate payments.  In no event shall the Participant, directly or indirectly, designate the calendar year of payment.  The Company may change or modify the terms of this Agreement without the Participant’s consent or signature if the Company determines, in its sole discretion, that such change or modification is necessary for purposes of compliance with or exemption from the requirements of Section 409A of the Code or any regulations or other guidance issued thereunder.  Notwithstanding the previous sentence, the Company may also amend the Plan or this Agreement or revoke the Stock Units to the extent permitted by the Plan.

13.French Participants.  If the Participant is a French Participant (as defined in the Rules of the Rhythm Pharmaceuticals, Inc. 2017 Equity Incentive Plan for Stock Options, Restricted Stock Units and Performance Units Granted to Participants in France) on the Date of Grant, the terms of the attached Addendum to the Award Agreement Relating to Performance Units Granted to French Participants pursuant to the 2017 Equity Incentive Plan shall apply to this Agreement and the Stock Units granted hereunder.

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In Witness Whereof, the parties have executed this Agreement as of the date first above written.

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[Signature Page to Rhythm Pharmaceuticals, Inc. Performance Unit Agreement]

RHYTHM PHARMACEUTICALS, INC.

ADDENDUM TO THE AWARD AGREEMENT RELATING TO PERFORMANCE UNITS GRANTED TO FRENCH PARTICIPANTS PURSUANT TO THE

2017 EQUITY INCENTIVE PLAN

In addition to the terms of the Plan and the Agreement, the grant of Performance Units to the French Participant is subject to the following additional specific terms and conditions (the “Addendum”).

Type of Grant. The Performance Units are granted as French-qualified Performance Units and are intended to qualify for the special tax and social security treatment applicable to shares of Stock granted for no consideration under Sections L. ▇▇▇-▇▇▇-▇ to L. ▇▇▇-▇▇▇-▇  and Sections L. 22-10-59 to L. 22-10-60 of the French Commercial Code, as amended.  The Performance Units are granted subject to the terms and conditions of the Rules of the Rhythm Pharmaceuticals, Inc. 2017 Equity Incentive Plan for Stock Options, Restricted Stock Units and Performance Units Granted to Participants in France (the “French Sub-Plan”).

Certain events may affect the status of the Performance Units as French-qualified Performance Units or the underlying Stock, and the Performance Units or the underlying Stock may be disqualified in the future.  The Company does not make any undertaking or representation to maintain the qualified status of the French-qualified Performance Units or of the underlying Stock as described in the French Sub-Plan.

Capitalized terms not defined herein, the Agreement or the Plan shall have the meanings ascribed to them in the French Sub-Plan.

Restrictions on Sale or Transfer of Shares.

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Except in the case of the Participant’s termination of employment due to death or Disability (as defined in the French Sub-Plan), the minimum mandatory holding period restriction will continue to apply even if the Participant is no longer an Employee or a Managing Corporate Officer of the Company or any Affiliate.

Termination of Service Due to Death.  In the event of the Participant’s death, the Participant’s heirs may request the issuance of the Stock underlying the Performance Units that have not vested prior to the Participant’s death subject to the Award within six months from the date of the Participant’s death, as provided for in Section III(c) of the French Sub-Plan and provided that such shares of Stock will not become transferable to the French Participant’s heirs unless, until and to the extent milestones relating to the performance-vesting conditions set forth in Appendix A to the Agreement are satisfied.  In any case, if the Participant’s heirs do not request the shares of Stock within six months from the date of the Participant’s death, the Award will be forfeited.

Settlement of RSUs. Subject to Section III(d) of the French Sub-Plan, Settlement of Performance Units will only be in shares of Stock.

Foreign Asset/Account Reporting Information.  If the Participant holds cash or shares of Stock outside of France or maintains a foreign bank or brokerage account (including accounts that were opened and closed during the tax year), the Participant is required to report such assets and accounts to the French tax authorities on an annual basis on a specified form, together with the Participant’s income tax return. Failure to complete this reporting can trigger significant penalties.

Use of English Language.  The Participant acknowledges and agrees that it is the Participant’s express wish that this Agreement, as well as all documents, notices and legal proceedings entered into, given or instituted pursuant hereto or relating directly or indirectly hereto, be drawn up in English.

Utilisation de la langue anglaise. Vous reconnaissez et acceptez qu’il est de votre volonté que le présent accord, ainsi que tout document, toute notification et toute procédure judiciaire conclue, reçue ou intentée en vertu des présentes ou s’y rapportant directement ou indirectement, soient rédigés en anglais.

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