Unifi (UFI) 10-K 2008 FY Annual report

Exhibit 32.1

CERTIFICATION PURSUANT TO 18 U.S.C. SECTION 1350,
AS ADOPTED PURSUANT TO
SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

In connection with the Unifi, Inc. (the “Company”) Annual Report on Form 10-K for the period ended June 29, 2008 as filed with the Securities and Exchange Commission on the date hereof (the “Report”), I, William L. Jasper, President and Chief Executive Officer of the Company, certify pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that:

(1)	The Report fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934, as amended; and
(2)	The information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

Date:	September 12, 2008	By:	/s/ WILLIAM L. JASPER
			William L. Jasper
			President and Chief Executive Officer