Lock-Up Agreement

EXHIBIT 2

Lock-Up Agreement

Rhythm Pharmaceuticals, Inc. Public Offering of Common Stock

May ___, 2017

Xxxxxx Xxxxxxx & Co. LLC

Xxxxxxx Lynch, Pierce, Xxxxxx & Xxxxx Incorporated

As Representatives of the several Underwriters, c/o Morgan Xxxxxxx & Co. LLC 0000 Xxxxxxxx Xxx Xxxx, XX 00000

Ladies and Gentlemen:

This letter is being delivered to you in connection with the proposed Underwriting Agreement (the “Underwriting Agreement”), between Rhythm Pharmaceuticals, Inc., a Delaware corporation, including any predecessor or successor company, as the case may be (the “Company”), and each of you as representatives of a group of Underwriters named therein (the “Underwriters”), relating to an underwritten public offering of shares of common stock (“Common Stock”), of the Company (the “Offering”).

In order to induce you and the other Underwriters to enter into the Underwriting Agreement, the undersigned will not, without the prior written consent of the Representatives, offer, sell, contract to sell, pledge or otherwise dispose of, (or enter into any transaction which is designed to, or might reasonably be expected to, result in the disposition (whether by actual disposition or effective economic disposition due to cash settlement or otherwise) by the undersigned or any affiliate of the undersigned or any person in privity with the undersigned or any affiliate of the undersigned), directly or indirectly, including the filing (or participation in the filing) of a registration statement (other than a registration statement on Form S-8) with the Securities and Exchange Commission (the “SEC”) in respect of, or establish or increase a put equivalent position or liquidate or decrease a call equivalent position within the meaning of Section 16 of the Securities Exchange Act of 1934, as amended (the “Exchange Act”), and the rules and regulations of the SEC promulgated thereunder with respect to, any capital stock of the Company or any securities convertible into, or exercisable or exchangeable for such capital stock, or publicly announce an intention to effect any such transaction, for a period from the date hereof until 180 days after the date of the Underwriting Agreement (the “Lock-up Period”).  If the undersigned is an officer or director of the Company, the undersigned further agrees that the foregoing restrictions shall be equally applicable to any issuer-directed shares of Common Stock the undersigned may purchase in the Offering.

The provisions of the immediately preceding paragraph shall not apply to (i) the sale of shares of Common Stock by the undersigned to the Underwriters pursuant to the Underwriting Agreement, (ii) transfers of shares of capital stock of the Company or any securities convertible into, or exercisable or exchangeable for such capital stock as a bona fide gift or gifts, (iii) transfers or dispositions of shares of capital stock of the Company or any securities convertible into, or exercisable or exchangeable for such capital stock to any trust for the direct or indirect benefit of the undersigned or the immediate family of the undersigned in transactions not involving a disposition for value; (iv) transfers or dispositions of shares of capital stock of the Company or any securities convertible into, or exercisable or exchangeable for such capital stock to any corporation, partnership, limited liability company or other entity all of the beneficial ownership interests of which are held by the undersigned or the immediate family of the undersigned in a transaction not involving a disposition for value; (v) transfers or dispositions of shares of capital stock of the Company or any securities convertible into, or exercisable or exchangeable for such capital stock by will, other testamentary document or intestate succession to the legal representative, heir, beneficiary or a member of the immediate family of the undersigned;

or (vi) distributions of shares of capital stock of the Company or any securities convertible into, or exercisable or exchangeable for such capital stock to partners, members or stockholders of the undersigned; provided, that in the case of any transfer, disposition or distribution pursuant to clause (ii), (iii), (iv), (v) or (vi), each transferee, donee or distributee shall execute and deliver to the Representatives a lock-up letter in the form of this letter; and provided further, that in the case of any transfer, disposition or distribution pursuant to clause (ii), (iii), (iv) or (vi), no filing by any party (donor, donee, transferor or transferee) under the Exchange Act or other public announcement reporting a reduction in the beneficial ownership of Common Stock held by the undersigned shall be required or shall be made voluntarily in connection with such transfer, disposition or distribution (other than a filing on a Form 5 made after the expiration of the 180-day period referred to in the immediately preceding paragraph).  For purposes of this letter, “immediate family” shall mean any relationship by blood, marriage, domestic partnership, or adoption, not more remote than first cousin.  Furthermore, notwithstanding the restrictions imposed by this letter, the undersigned may, without the prior written consent of the Representatives, (a) exercise an option to purchase shares of Common Stock granted under any equity incentive plan or equity purchase plan of the Company which is described in the registration statement relating to the Offering, provided that the underlying equity securities shall continue to be subject to the restrictions on transfer set forth in this letter, (b) establish a trading plan pursuant to Rule 10b5-l under the Exchange Act for the transfer of shares of Common Stock, provided that such plan does not provide for any transfers of Common Stock, and no filing with the SEC or other public announcement shall be required or voluntarily made by the undersigned or any other person in connection therewith, in each case during the 180-day period referred to in the immediately preceding paragraph, (c) transfer shares of Common Stock to the Company in connection with the termination of the undersigned’s employment with the Company, and (d) transfer or dispose of shares of Common Stock purchased in the Offering from the Underwriters (other than any issuer-directed shares of Common Stock purchased in the Offering by an officer or director of the Company) or on the open market following the Offering; provided that, in the case of clauses (b), (c) and (d) above, no filing with the SEC or other public announcement shall be required or voluntarily made by the undersigned or any other person in connection therewith, in each case during the 180-day period referred to in the immediately preceding paragraph, other than in the case of clause (c) to the extent such filing is required and the employment termination is footnoted or otherwise disclosed therein.

If the undersigned is an officer or director of the Company, (i) the Representatives agree that, at least three business days before the effective date of any release or waiver of the foregoing restrictions in connection with a transfer of shares of Common Stock, the Representatives will notify the Company of the impending release or waiver, and (ii) the Company has agreed in the Underwriting Agreement to announce the impending release or waiver by press release through a major news service at least two business days before the effective date of the release or waiver.  Any release or waiver granted by the Representatives hereunder to any such officer or director shall only be effective two business days after the publication date of such press release.  The provisions of this paragraph will not apply if (a) the release or waiver is effected solely to permit a transfer not for consideration and (b) the transferee has agreed in writing to be bound by the same terms described in this letter to the extent and for the duration that such terms remain in effect at the time of the transfer.

This letter shall automatically terminate and the undersigned shall be released from all obligations under this letter upon the earliest to occur, if any, of (i) either the Company, on the one hand, or the Representatives, on the other hand, advising the other in writing, prior to the execution of the Underwriting Agreement, that they have determined not to proceed with the Offering, (ii) the Underwriting Agreement being terminated prior to the Closing Date (as defined in the Underwriting Agreement), (iii) the registration statement filed with the SEC with respect to the Offering being withdrawn and (iv) December 31, 2017, in the event that the Underwriting Agreement has not been executed by such date.

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	OrbiMed Private Investments V, LP
	By:	OrbiMed Capital GP V LLC, its General Partner
		By:	OrbiMed Advisors LLC, its Managing Member
		By:	/s/ Xxxxxxxx X. Xxxxxxxxxxx
			Name:	Xxxxxxxx X. Xxxxxxxxxxx
			Title:	Member