Exhibit 99.1

NEWS RELEASE

FOR IMMEDIATE RELEASE

Contact: Kristine Boyd

(713) 688-9600 x 135

FRONTIER ANNOUNCES CONSENT SOLICITATION

Houston—May 13, 2011—Frontier Oil Corporation (NYSE: FTO) announced today that it has commenced a solicitation of consents from holders of its 8.5% Senior Notes due 2016 in aggregate principal amount outstanding of $200 million and from its 6.875% Senior Notes due 2018 in aggregate principal amount outstanding of $150 million to effect proposed amendments to the indentures governing the notes.

Frontier previously entered into an Agreement and Plan of Merger, dated as of February 21, 2011 (the “Merger Agreement”), by and among Frontier, North Acquisition, Inc. and Holly Corporation (“Holly”), pursuant to which Frontier would become a wholly owned subsidiary of Holly (the “Merger”). No consent of any holder of any notes is required to consummate the Merger.

The management teams of Frontier and Holly have been evaluating and expect to continue evaluating an internal restructuring of certain Holly and Frontier legal entities after completing the Merger, which may include an internal merger of Frontier into Holly. If this internal merger is consummated, Holly would assume the obligations under Frontier’s notes and indentures, and certain of Holly’s subsidiaries would provide guarantees of the notes as required under the Frontier indentures.

Holly Energy Partners, L.P., a publicly traded limited partnership in which Holly has a 34% ownership interest and indirectly owns the general partner (“HEP”), is currently an unrestricted subsidiary under an indenture governing the outstanding senior notes of Holly. The proposed amendments to the Frontier indentures would designate HEP and its subsidiaries as “unrestricted subsidiaries” under the indentures and would except those entities and certain affiliates from certain covenant restrictions contained in the indentures so as to better facilitate a successful integration of Holly and Frontier, as well as make certain other amendments with respect to the transactions with affiliates and additional guarantor covenants. The proposed amendments, if they become operative, would substantially conform the treatment of HEP and its subsidiaries under Frontier’s indentures to the treatment of such entities under the indenture governing the outstanding senior notes of Holly.

The terms and conditions of the consent solicitations are described in a Consent Solicitation Statement dated May 13, 2011 and a related Consent Form. Frontier will pay a consent fee in the amount of $1.25 per $1,000 principal amount of the notes for valid consents received from holders of record of notes as of 5:00 p.m., New York City time, on May 12, 2011, with such consent fee being paid promptly after the effectiveness of the Merger. If the proposed amendments are approved and supplemental indentures entered into by Frontier, the supplemental indentures would bind all holders of the respective notes, including those that did not give their consent, but non-consenting holders would not receive the consent fee.

The consent solicitation is scheduled to expire at 5:00 p.m., New York City time, on May 26, 2011, unless extended or earlier terminated. The consent solicitation is subject to the satisfaction of certain conditions, including Frontier’s receipt of consents representing a majority of the holders of each series of notes from whom consent is sought, as well as other customary conditions.

Frontier has engaged UBS Investment Bank to act as the solicitation agent in connection with the consent solicitation. Questions regarding the consent solicitation or requests for documentation may be directed to UBS Investment Bank at (888) 719-4210.

This announcement is not a solicitation of consent with respect to any notes. The consent solicitation is being made solely by the Consent Solicitation Statement dated May 13, 2011 and the related Consent Form.

The Company

Frontier operates a 135,000 bpd refinery located in El Dorado, Kansas, and a 52,000 bpd refinery located in Cheyenne, Wyoming, and markets its refined products principally along the eastern slope of the Rocky Mountains and in other neighboring plains states. Information about the Company may be found on its website at www.frontieroil.com.

Important Information for Investors and Shareholders

This press release does not constitute an offer to sell or the solicitation of an offer to buy any securities or a solicitation of any vote or approval. The issuance of Holly common stock in connection with the proposed Merger will be submitted to Holly’s stockholders for their consideration, and the proposed Merger will be submitted to shareholders of Frontier for their consideration. Holly has filed with the Securities and Exchange Commission (“SEC”) a registration statement on Form S-4 that includes a joint proxy statement to be used by Holly and Frontier to solicit the required approval of their shareholders in connection with the proposed Merger and constituted a prospectus of Holly. Holly and Frontier may also file other documents with the SEC concerning the proposed Merger. INVESTORS AND SECURITY HOLDERS OF HOLLY AND FRONTIER ARE URGED TO READ THE JOINT PROXY STATEMENT/PROSPECTUS REGARDING THE PROPOSED MERGER AND OTHER RELEVANT DOCUMENTS FILED WITH THE SEC CAREFULLY AND IN THEIR ENTIRETY WHEN THEY BECOME AVAILABLE BECAUSE THEY WILL CONTAIN IMPORTANT INFORMATION ABOUT THE PROPOSED MERGER. Investors and security holders may obtain a free copy of the joint proxy statement/prospectus and other documents containing important information about Holly and Frontier through the website maintained by the SEC at www.sec.gov. Copies of the documents filed with the SEC by Holly will be available free of charge on Holly’s website at www.hollycorp.com under the tab “Investors” or by contacting Holly’s Investor Relations Department at (214) 871-3555. Copies of documents filed with the SEC by Frontier will be available free of charge on Frontier’s website at www.frontieroil.com under the tab “Investor Relations” and then under the tab “SEC Filings” or by contacting Frontier’s Investor Relations Department at (713) 688-9600.

Holly, Frontier and certain of their respective directors and executive officers may be deemed to be participants in the solicitation of proxies from the stockholders of Holly and shareholders of Frontier in connection with the proposed Merger. Information about the directors and executive officers of Holly is set forth in its proxy statement for its 2011 annual meeting of stockholders, which was filed with the SEC on March 31, 2011. Information about the directors and executive officers of Frontier is set forth in its proxy statement for its 2011 annual meeting of shareholders, which was filed with the SEC on March 21, 2011. These documents can be obtained free of charge from the sources indicated above. Other information regarding the participants in the proxy solicitation and a description of their direct and indirect interests, by security holdings or otherwise, are contained in the joint proxy statement/prospectus and other relevant materials to be filed with the SEC.

Cautionary Statement Regarding Forward-Looking Statements

This press release contains “forward-looking” statements within the meaning of Section 27A of the Securities Act of 1933 and Section 21E of the Securities Exchange Act of 1934. These include statements regarding the effects of the proposed Merger and statements preceded by, followed by or that otherwise include the words “believes,” “expects,” “anticipates,” “intends,” “estimates,” or similar expressions. Forward looking statements relating to expectations about future results or events are based upon information available to Frontier as of today’s date, and are not guarantees of the future performance of Holly, Frontier or the combined company, and actual results may vary materially from the results and expectations discussed. For instance, there is no assurance that the proposed Merger or any internal restructuring will be consummated by a specified date or at all. The Merger Agreement will terminate if the companies do not receive the necessary approval of Holly’s stockholders or Frontier’s shareholders or government approvals or if either Holly or Frontier fails to satisfy conditions to closing. Additional risks and uncertainties related to the proposed Merger include, but are not limited to, the successful integration of Holly’s and

Frontier’s businesses and the combined company’s ability to compete in the highly competitive refining and marketing industry. The revenues, earnings and business prospects of Holly, Frontier and the combined company and their ability to achieve planned business objectives will be subject to a number of risks and uncertainties. These risks and uncertainties include, among other things, risks and uncertainties with respect to the actions of actual or potential competitive suppliers of refined petroleum products in Holly’s, Frontier’s and the combined company’s markets; the demand for and supply of crude oil and refined products; the spread between market prices for refined products and market prices for crude oil; the possibility of constraints on the transportation of refined products; the possibility of inefficiencies, curtailments or shutdowns in refinery operations or pipelines; effects of governmental and environmental regulations and policies; the availability and cost of financing; the effectiveness of capital investments and marketing strategies; efficiency in carrying out construction projects; the ability to acquire refined product operations or pipeline and terminal operations on acceptable terms and to integrate any existing or future acquired operations; the possibility of terrorist attacks and the consequences of any such attacks; and general economic conditions.

Frontier cautions that the foregoing list of risks and uncertainties is not exclusive. Additional information concerning these and other risks is contained in Holly’s and Frontier’s most recently filed Annual Report on Form 10-K, subsequent Quarterly Report on Form 10-Q, recent Current Reports on Form 8-K and other SEC filings. All subsequent written and oral forward-looking statements concerning Holly, Frontier, the proposed Merger or other matters and attributable to Holly or Frontier or any person acting on their behalf are expressly qualified in their entirety by the cautionary statements above. Frontier undertakes no obligation to publicly update any of these forward-looking statements to reflect events or circumstances that may arise after the date hereof.