Exhibit 32.1

Certification of

Chief Executive Officer

of First Financial Bankshares, Inc.

This certification is provided pursuant to Section 906 of the Sarbanes-Oxley Act of 2002 (subsections (a) and (b) of Section 1350, Chapter 63 of Title 18, United States Code) and accompanies the annual report on Form 10-K (the “Form 10-K”) for the year ended December 31, 2019 of First Financial Bankshares, Inc. (the “Issuer”).

I, F. Scott Dueser, the Chairman of the Board, President and Chief Executive Officer of the Issuer certify, to the best of my knowledge, that:

1. the Form 10-K fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934 (15 U.S.C. 78m(a) or 78o(d)); and

2. the information contained in the Form 10-K fairly presents, in all material respects, the financial condition and results of operations of the Issuer.

Dated: February 14, 2020
	By:	/s/ F. SCOTT DUESER
		F. Scott Dueser
		Chairman of the Board, President and Chief Executive Officer

Subscribed and sworn to before me this 14th day of February, 2020.

/s/ Melissa A. Fenton

Notary Public

My commission expires: October 11, 2020