Offer Letter, dated December 21, 2017, by and between the Company and Hunter C. Smith

rhythm

Rhythm Pharmaceuticals, Inc. 500 Boylston Street - 11th Floor Boston, MA 02116

Main Telephone: 617 ###-###-#### www.rhythmtx.com

December 21, 2017 Hunter Smith

c/o Rhythm Pharmaceuticals, Inc. 500 Boylston Street, 11th Floor Boston, MA 02116

Dear Hunter:

On behalf of Rhythm Pharmaceuticals, Inc., (the "Company" or "Rhythm"), I am pleased to set forth below the amended and restated terms of your employment with the Company. You and Rhythm previously were parties to the employment offer letter dated as of July 17, 2017, which was amended and restated on September 13, 2017. This second amended and restated employment offer letter amends and restates the terms of that September 13, 2017 offer letter in its entirety.

Employment. You are currently the Chief Financial Officer of the Company, beginning  on  July 31,  2017, and during the term of your employment with the Company, you will continue to hold the position and title of Chief Financial Officer, reporting to Keith Gottesdiener, CEO. During the term of your employment with the Company, you will be responsible for performing the duties associated with the position above or as the Company may otherwise assign to you. Your primary place of employment initially will be in the Company's offices located in Boston, Massachusetts; however, you will  be expected to travel as may be necessary to fulfill your responsibilities. In the course of your employment with the Company, you will be subject to, and required to comply with, all Company policies and all applicable laws and regulations.

Signing Bonus. Prior to the date of this letter, the Company has paid to you, and you have received, a one-time cash signing bonus of $27,000, which signing bonus was taxable to you.

Base Salary. During your employment, your salary will be $380,000 annualized, subject to all required and elected taxes and other withholdings. Your salary may be adjusted from time to time in accordance with normal business practice and in the sole discretion of the Company.

Annual Incentive Bonus. Following the end of each fiscal year and subject to the approval by the Company's Board of Directors, you will be eligible to earn an incentive bonus, based on  your performance and the Company's performance, each during the applicable fiscal year, if your employment continues in good standing on the date of payment of such incentive bonus. Your target annual incentive bonus opportunity shall be 35% of your annualized base salary.

Equity Grant. Any existing grants of equity you have in the Company will be treated consistent with the terms of the applicable agreements under which such awards have been granted. You may be awarded additional equity grants from time to time in accordance with normal business practice and in the sole discretion of the Company's Board of Directors. The terms of any future equity grant will be consistent with any plan under which they are granted and the terms of the applicable agreement for the award(s).

Relocation Expenses· Allowance. Rhythm agrees to pay you $173,151.84 to reimburse you for travel, commuting, lodging and other relocation expenses (including moving your family to Boston if you decide to do so) for a period of two years commencing on January 1, 2018. Such $173,151.84 will  be paid  to you by the Company in equal monthly installments of $7,214.66 in accordance with the Company's ordinary payroll practices, beginning on the first payroll date following January 1,  2018 and continuing for a period of 24 months thereafter. You acknowledge that this relocation expenses allowance will be taxable to you.

Benefits. You may participate in any and all benefit programs that the Company establishes and makes available to its employees from time to time, subject to the terms and conditions of those programs. The Company's benefits programs are subject to change at any time in the Company's sole discretion.

Vacation. You will be entitled to annual paid vacation of four (4) weeks. Your accrual and use of  vacation time will be pursuant to any vacation or time off policy the Company may establish or modify from time to time. The Company's vacation policy is subject  to change  at any time in the Company's  sole discretion.

Outside Board Duties. You currently serve as an independent director of the NYSE listed multinational Genessee &  Wyoming Inc. ("Genessee"), and as a member of its Governance/Nominating Committee. You may remain as a director of Genessee, provided that your duties in such director role shall not in any way interfere with your role and duties as Chief Financial Officer of, and commitments to, the Company which shall supersede and take priority in any and all respects. Moreover, you agree that you will not be permitted to take on any additional director, board observer, advisory, consulting, or other such roles or commitments without the express prior written consent of the Chief Executive Officer of the Company.

Severance. If the Company terminates your employment without Cause (as defined below) or you resign your employment with the Company for Good Reason (as defined below) (in either event, a "Qualifying Termination"), then, subject to your execution of a reasonable release acceptable to the Company (the "Release"), the expiration of any revocation period provided in the Release and your continued compliance with the terms of the NDA (as defined below), the Company will pay you an amount (the "Regular Severance Amount") equal to your then-current base salary rate for a period of six (6) months, provided that, (i) if any such Qualifying Termination occurs at any time after the IPO, if any, the Regular Severance Amount shall be an amount equal to your then-current base salary rate for a period of nine (9) months and (ii) if any such Qualifying Termination occurs on, or at any time prior to, the first anniversary of the start date of your employment with the Company (even if such first anniversary occurs after the IPO), the Regular Severance Amount shall be an amount equal to your then-current base salary rate for a period of twelve (12) months.

If there is a Qualifying Termination within the three (3) months immediately preceding or the twelve (12) months immediately following a Change of Control (as defined in the Company's 2015 Equity Incentive

Plan, as may be amended and in effect from time to time or succeeded or superseded by a successor equity incentive plan), then, subject to your execution of a Release following your Separation from Service (as defined below), the expiration of any revocation period provided in the Release and your continued compliance with the terms of the NDA, the Company will pay you in lieu of any Regular Severance Amount, an amount (the "Change of Control Severance Amount") equal to your then-current base salary rate for a period of twelve (12) months plus an amount equal to 100% of your then-applicable target annual incentive bonus.

Any severance amount to which you may be entitled under this letter will be paid in substantially equal installments in accordance with the Company's ordinary payroll practices, beginning on the first payroll date following the date that is either (i) sixty (60) days after the date of your Separation from Service or

(ii) in the case of a Separation from Service that is a Qualifying Termination that occurs within three (3) months immediately preceding a Change of Control, sixty (60) days after such Change of Control, provided that, in the case of either of the foregoing clauses (i) and (ii), the Company, in its sole discretion, may have the option to pay any such severance amount to you as a lump sum.  To be eligible for either  the Regular Severance Amount or the Change of Control Severance Amount, as applicable, you must execute and deliver the Release to the Company and allow it to become effective within thirty (30) days  of your Separation from Service or, if later, within thirty (30) days of a Change of Control giving rise to a Change of Control Severance Amount entitlement.

In addition, if following your Separation from Service, you are eligible for and timely elect continued medical insurance coverage pursuant to COBRA, the Company will reimburse you for the applicable premiums for you and your eligible dependents during the period commencing on the date of your Separation from Service and ending on the earlier to occur of (a) the final day of the applicable severance period and (b) the date you otherwise become ineligible for continued coverage under COBRA. Notwithstanding the foregoing, if the Company determines that it cannot provide such reimbursement of premiums to you without potentially violating applicable law, the Company shall not be obligated  to make any such payments or reimbursements to you.

If the Qualifying Termination occurs within the three (3) months immediately preceding or the twelve

(12) months immediately following a Change of Control, then each outstanding equity award in the Company held by you shall immediately vest and, if applicable, become exercisable with respect to one hundred percent (100%) of the shares of equity of the Company subject thereto. The foregoing provisions of this paragraph shall apply notwithstanding anything express or implied to the contrary in any agreement or award between you and the Company, or in any plan of the Company, that is applicable to such outstanding equity award.

Notwithstanding anything herein to the contrary, in the event that any compensation or benefit that constitutes "nonqualified deferred compensation" within the meaning of Section 409A of the Internal Revenue Code of 1986, as amended (the "Code"), becomes payable upon the occurrence of a Change of Control, such compensation or benefit shall not be paid unless such Change of Control constitutes a "change in control event" within the meaning of Section 409A of the Code.

If any payment or benefit you would receive under this letter, when combined with any other payment or benefit you receive pursuant to the termination of your employment with the Company ("Payment") would (i) constitute a "parachute payment" within the meaning of Section 280G of the Code, and (ii) but

for this sentence, be subject to the excise tax imposed by Section 4999 of the Code (the "Excise Tax"), then such Payment shall be either (x) the full amount of such Payment or (y) such lesser amount (with your choice of whether to reduce cash payments or stock option compensation or both) as would result in no portion of the Payment being subject to the Excise Tax, whichever of the foregoing amounts, taking into account the applicable federal, state and local employment taxes, income taxes and the Excise Tax results in your receipt, on an after-tax basis, of the greater amount of the Payment notwithstanding that all or some portion of the Payment may be subject to the Excise Tax.

Definitions

Separation from Service. For purposes of this letter, "Separation from Service" means  a "separation from service" within the meaning of Section 409A of the Code. Each installment payment provided under this letter shall at all times be considered a separate and distinct payment for purposes of Section 409A of the Code. Notwithstanding anything in this letter to the contrary, to the extent required to avoid a prohibited distribution under Section 409A of the Code, the benefits provided under this letter will not be provided to you until the earlier of (a) the expiration of the six-month period measured from the date of your Separation from Service with the Company or (b) the date of your death. Upon the first business day after expiration of the relevant period, all payments delayed pursuant to the preceding sentence will be paid in a lump sum and any remaining payments due will be paid as otherwise provided herein.

Cause. "Cause" shall mean the occurrence of any of the following events by the individual: (i) commission of any crime involving the Company, or any crime involving fraud, breach of trust, or physical or emotional harm to any person, moral turpitude or dishonesty; (ii) any unauthorized use or disclosure of the Company's proprietary information (other than any such use or disclosure that is not intentional and is not material); (iii) any intentional misconduct or gross negligence that has a material adverse effect on the Company's business or reputation; (iv) any material breach by you of any agreement between you and the Company that is not cured within thirty (30) days after receipt of written notice from the Company describing any such breach; or (v) repeated and willful failure to perform the duties, functions and responsibilities of the individual's position after a written warning from the Company.

Good Reason. "Good Reason" shall mean your resignation from all positions you then hold with the Company if: (A) without your written consent (i) there is a material diminution in the nature or scope of your responsibilities, duties, authority, or title; (ii) there is a material reduction of your base salary; provided, however, that a material reduction in your base salary pursuant to a salary reduction program affecting all or substantially all of the employees of the Company and that does not adversely affect  you to a greater extent than other similarly situated employees shall not constitute Good Reason; or (iii) you are required to relocate your primary work location to a facility or location that would increase your one way commute distance by more than thirty-five (35) miles from your primary work location as of immediately prior to such change, (B) you provide written notice outlining such conditions, acts or omissions to the Company's Chief Executive Officer, President, or General Counsel within  thirty (30) days immediately following such material change or reduction, (C) such material change or reduction is not remedied by the Company within thirty (30) days following the Company's receipt of such written notice and (D) your resignation is effective not later than thirty (30) days after the expiration of such  thirty (30) day cure period. "Good Reason" shall also mean your resignation, at your sole discretion,  on the one year anniversary of a Change of Control from all positions you then hold with the Company or its

successor if by that date (i) you have not entered into a written letter or agreement with the Company or such successor that provides for your continued employment with the Company or such successor, and

(ii) if at that one year anniversary of a Change of Control, another Chief Financial Officer has any control and/or oversight, directly or indirectly, over the Company (or what used to be the Company prior to such transaction). For purposes of clarification, any Qualifying Termination that occurs on the  first  anniversary of a Change of Control shall be deemed and treated as occurring within the twelve (12) months immediately following a Change of Control for all purposes of this letter.

Invention, Non-Disclosure, Non-Competition and Non-Solicitation Obligations. You previously have executed and delivered the Company's standard form of Employee Proprietary Information, Inventions, Non-Competition and Non-Solicitation Agreement (the "NDA"), an executed copy of which is attached hereto as Exhibit A.

At-Will Employment. This letter shall not be construed as an agreement, either express or implied, to employ you for any stated term, and shall in no way alter the Company's policy of employment at-will. Similarly, nothing in this letter shall be construed as an agreement, either express or implied, to pay you any compensation or grant you any benefit beyond the end of your employment with  the Company, except as otherwise explicitly set forth in this letter. This letter supersedes all prior understandings, whether written or oral, including, without limitation, your current employment agreement, with respect  to the subject matter of this letter.

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rhythm

Please indicate  your acceptance  of this letter agreement  by signing below in the space provided for your signature.

Sincerely,

/S/ Keith Gottesdiener

Keith M. Gottesdiener

Chief Executive Officer

The foregoing correctly sets forth the terms of my at-will employment with the Company.  I am not

relying on any representations other than those set forth above.

/S/Hunter SmithJanuary 22, 2018___________

Hunter SmithDate