POWER OF ATTORNEY

        Know all by these presents, that the undersigned hereby constitutes and
appoints each of Jolie M. Siegel, Kendra Adams, Shagha T. Russell, Andrew J.
Hirsch, Shoaib Ghias and Nathan Needle, signing singly, the undersigned's true
and lawful attorney-in-fact to:

        (1) execute for and on behalf of the undersigned, in the undersigned's
            capacity as an officer and/or director of C4 Therapeutics, Inc. (the
            "Company"), (i) Form ID, including any attached documents, to effect
            the assignment of codes to the undersigned to be used in the
            transmission of information to the United States Securities and
            Exchange Commission using the EDGAR System, (ii) Forms 3, 4 and 5,
            (iii) Schedule 13D, (iv) Schedule 13G and (v) amendments of each
            thereof, in accordance with Section 16(a) of the Securities Exchange
            Act of 1934, as amended, and the rules thereunder;

        (2) do and perform any and all acts for and on behalf of the undersigned
            which may be necessary or desirable to complete and execute any such
            Form 3, 4 or 5, Schedule 13D, Schedule 13G or any amendments thereto
            and timely file such form with the United States Securities and
            Exchange Commission and any stock exchange or similar authority; and

        (3) take any other action of any type whatsoever in connection with the
            foregoing which, in the opinion of such attorney-in-fact, may be of
            benefit to, in the best interest of, or legally required by, the
            undersigned, it being understood that the documents executed by such
            attorney-in-fact on behalf of the undersigned pursuant to this Power
            of Attorney shall be in such form and shall contain such terms and
            conditions as such attorney-in-fact may approve in such attorney-in-
            fact's discretion.

        The undersigned hereby grants to each such attorney-in-fact full power
and authority to do and perform any and every act and thing whatsoever
requisite, necessary, or proper to be done in the exercise of any of the rights
and powers herein granted, as fully to all intents and purposes as the
undersigned might or could do if personally present, with full power of
substitution or revocation, hereby ratifying and confirming all that such
attorney-in-fact, or such attorney-in-fact's substitute or substitutes, shall
lawfully do or cause to be done by virtue of this Power of Attorney and the
rights and powers herein granted. The undersigned acknowledges that the
foregoing attorneys-in-fact, in serving in such capacity at the request of the
undersigned, are not assuming, nor is the Company assuming, any of the
undersigned's responsibilities to comply with Section 16 or Regulation 13D-G of
the Securities Exchange Act of 1934, as amended. The undersigned hereby agrees
to indemnify the attorney-in-fact and the Company from and against any demand,
damage, loss, cost or expense arising from any false or misleading information
provided by the undersigned to the attorney-in-fact.

        This Power of Attorney shall remain in full force and effect until the
undersigned is no longer required to file Forms 3, 4 and 5 with respect to the
undersigned's holdings of and transactions in securities issued by the Company,
unless earlier revoked by the undersigned in a signed writing delivered to the
foregoing attorneys-in-fact. This Power of Attorney may be filed with the United
States Securities and Exchange Commission as a confirming statement of the
authority granted herein. This Power of Attorney supersedes any prior power of
attorney in connection with the undersigned's capacity as an officer and/or
director of the Company. This Power of Attorney shall expire as to any
individual attorney-in-fact if such attorney-in-fact ceases to be an executive
officer of the Company.

        IN WITNESS WHEREOF, the undersigned has caused this Power of Attorney to
be executed as of August 31, 2023.

/s/ Mark Mossler
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Name: Mark Mossler