Exhibit 32.1

CERTIFICATION OF CHIEF EXECUTIVE
OFFICER OF HOLLY CORPORATION
PURSUANT TO 18 U.S.C. SECTION 1350

     In connection with the accompanying report on Form 10-Q for the nine months ended September 30, 2004 and filed with the Securities and Exchange Commission on the date hereof (the “Report”), I, C. Lamar Norsworthy, III, Chief Executive Officer of Holly Corporation (the “Company”) hereby certify, 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; 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: November 8, 2004	/s/ C. Lamar Norsworthy, III
	C. Lamar Norsworthy, III
	Chairman of the Board and Chief Executive Officer