Exhibit 5.1

October 29, 2021

CM Life Sciences III Inc.

c/o Corvex Management LP

667 Madison Avenue
New York, New York 10065

Ladies and Gentlemen:

We have acted as New York counsel to CM Life Sciences III Inc., a corporation organized under the laws of Delaware (“CMLS III” or the “Company”), in connection with the preparation and filing of the Company’s Registration Statement on Form S-4 (the “Registration Statement,” which term does not include any other document or agreement whether or not specifically referred to or incorporated by reference therein or attached as an exhibit or schedule thereto), including the proxy statement/prospectus forming a part thereof, relating to the Company’s shares of Class A common stock, par value $0.0001 per share (the “CMLS III Shares”), to be issued by the Company, pursuant to the terms of the Agreement and Plan of Merger, dated as of August 5, 2021, by and among the Company, Clover III Merger Sub Inc. (“Merger Sub”) and EQRx, Inc. (“EQRx”) (the “Merger Agreement”) and the transactions contemplated thereby (the “Business Combination”). Unless otherwise indicated, each capitalized term used herein has the meaning ascribed to it in the Registration Statement.

In connection with our opinions expressed below, we have examined originals or copies certified to our satisfaction of the following documents and such other documents, certificates and other statements of government officials and corporate officers of the Company as we deemed necessary for the purposes of the opinions set forth in this opinion letter: (i) the Registration Statement; (ii) the Merger Agreement; (iii) the form of certificate of incorporation of the Company to become effective upon consummation of the Business Combination; (iv) the form of bylaws of the Company to become effective upon consummation of the Business Combination; and (v) the specimen Class A common stock certificate of the Company. We have also examined the originals, or copies, of such corporate records, agreements, documents and other instruments and have made such other investigations as we have deemed relevant and necessary in connection with this opinion letter. As to questions of fact material to this opinion letter, we have relied, with your approval, upon oral and written representations of the Company and certificates or comparable documents of public officials and of officers and representatives of the Company.

In making such examination and rendering such opinions, we have assumed without independent investigation or verification of any kind the genuineness of all signatures, the legal capacity of all natural persons signing all documents, the authenticity of all documents submitted to us as originals, the conformity to authentic original documents of all documents submitted to us as copies, the truthfulness, completeness and correctness of all factual representations and statements contained in all documents, and the accuracy and completeness of all public records examined by us.

Based upon the foregoing assumptions, and subject to the qualifications set forth in this opinion letter, having considered such questions of law as we have deemed necessary as a basis for the opinion expressed below, we are of the opinion that the CMLS III Shares to be issued by the Company pursuant to and in the manner contemplated by the terms of the Merger Agreement will be, upon issuance, duly authorized and, when the CMLSIII Shares have been issued upon the terms and conditions set forth in the Registration Statement and the Merger Agreement, such CMLS III Shares will be validly issued, fully paid and nonassessable.

We are members of the bar of the State of New York. The Company is a Delaware corporation, and we have not considered, and we express no opinion as to, any law other than the General Corporation Law of the State of Delaware.

We hereby consent to be named in the Registration Statement and in the related proxy statement/prospectus contained therein as the attorneys who passed upon the legality of the CMLS III Shares to be issued pursuant to the Registration Statement and to the filing of a copy of this opinion letter as Exhibit 5.1 to the Registration Statement. In giving such consent, we do not hereby admit that we are in the category of persons whose consent is required under Section 7 of the Securities Act of 1933, as amended, and the rules and regulations of the Securities and Exchange Commission promulgated thereunder. The opinions expressed above are as of the date hereof only, and we assume no responsibility to update this opinion letter, or to advise you of, any such facts or circumstances of which we become aware, regardless of whether or not they affect the opinions expressed in this opinion letter. 

Very truly yours,

/s/ White & Case LLP