Dillard's (DDS) 10-Q 2010 Q3 Quarterly 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 Quarterly Report of Dillard’s, Inc. (the “Company”) on Form 10-Q for the period ended October 31, 2009 as filed with the Securities and Exchange Commission on the date hereof (the “Report”), I, William Dillard, II, Chairman of the Board 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) and 15(d) of the Securities Exchange Act of 1934; and

(2) The information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

Dated: December 3, 2009

/s/ William Dillard, II

William Dillard, II

Chairman of the Board and Chief Executive Officer