First Financial Bankshares (FFIN) 10-K 2010 FY Annual report

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, 2010 of First Financial Bankshares, Inc.

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

1. the Form 10-K fully complies with the requirements of section 13(a) or section 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 Company.

Dated: February 24, 2011

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

Subscribed and sworn to before me this 24th day of February, 2011.

/s/ Gaila N. KilpatrickGaila N. Kilpatrick

Notary Public

My commission expires: April 15, 2013