EX-5.1

Exhibit 5.1

LOGO

Alan Hambelton

T: +1 206 452 8756

ahambelton@cooley.com

March 28, 2024

Eliem Therapeutics, Inc.

PMB #117

2801 Centerville Road 1^st Floor

Wilmington, DE 19808-1609

Ladies and Gentlemen:

We have acted as counsel to Eliem Therapeutics, Inc., a Delaware corporation (the “Company”), in connection with the filing by the Company of a Registration Statement on Form S-8 (the “Registration Statement”) with the Securities and Exchange Commission (the “Commission”) covering the offering of up to 1,661,966 shares (the “Shares”) of the Company’s Common Stock, par value $0.0001 per share (“Common Stock”), consisting of (i) 1,384,972 shares of Common Stock issuable pursuant to the Company’s 2021 Equity Incentive Plan (the “2021 Plan”), and (iii) 276,994 shares of Common Stock issuable pursuant to the Company’s 2021 Employee Stock Purchase Plan (together with the 2021 Plan, the “Plans”).

In connection with this opinion, we have examined and relied upon (a) the Registration Statement and the related prospectuses, (b) the Company’s certificate of incorporation and bylaws, each as currently in effect, (c) the Plans, and (d) such other records, documents, opinions, certificates, memoranda and instruments as in our judgment are necessary or appropriate to enable us to render the opinion expressed below. We have assumed the genuineness of all signatures, the authenticity of all documents submitted to us as originals, the conformity to originals of all documents submitted to us as copies, the accuracy, completeness and authenticity of certificates of public officials, and the due authorization, execution and delivery of all documents by all persons other than the Company where authorization, execution and delivery are prerequisites to the effectiveness thereof. As to certain factual matters, we have relied upon a certificate of an officer of the Company and have not independently verified such matters.

Our opinion is expressed only with respect to the General Corporation Law of the State of Delaware. We express no opinion to the extent that any other laws are applicable to the subject matter hereof and express no opinion and provide no assurance as to compliance with any federal or state securities law, rule or regulation.

On the basis of the foregoing, and in reliance thereon, we are of the opinion that the Shares, when sold and issued in accordance with the Plans, the Registration Statement and the related prospectuses, will be validly issued, fully paid and nonassessable (except as to shares issued pursuant to deferred payment arrangements, which will be fully paid and nonassessable when such deferred payments are made in full).

This opinion is limited to the matters expressly set forth in this letter, and no opinion should be implied, or may be inferred, beyond the matters expressly stated. This opinion speaks only as to law and facts in effect or existing as of the date hereof and we have no obligation or responsibility to update or supplement this opinion to reflect any facts or circumstances that may hereafter come to our attention or any changes in law that may hereafter occur.

Cooley LLP 1700 Seventh Avenue, Suite 1900, Seattle, WA 98101

Phone: (206) 452-8700 Fax: (206) 452-8800 Cooley.com


Sincerely,

Cooley LLP

By:		/s/ Alan D. Hambelton
		Alan D. Hambelton