First Financial Bankshares (FFIN) 10-Q 2009 Q3 Quarterly 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 quarterly report on Form 10-Q (the “Form 10-Q”) for the quarter ended September 30, 2009 of First Financial Bankshares, Inc.

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

1. the Form 10-Q 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-Q fairly presents, in all material respects, the financial condition and results of operations of the Company.

Dated: November 3, 2009

By:	/s/ F. SCOTT DUESER
	F. Scott Dueser
	Chief Executive Officer

Subscribed and sworn to before me this 3rd of November, 2009.

/s/ Gaila N. KilpatrickGaila N. Kilpatrick

Notary Public

My commission expires: April 15, 2013