Exhibit 99.1

Holly Energy Partners, L.P. and Holly Energy Finance Corp.

Announce Tender Offer and Consent Solicitation

DALLAS, TX, February 27, 2012 — Holly Energy Partners, L.P. (NYSE:HEP) and Holly Energy Finance Corp. (together, “Holly Energy”) announced that they have commenced a cash tender offer (the “Tender Offer”) to purchase any and all of its outstanding $185.0 million aggregate principal amount of its 6.25% Senior Notes due 2015 (the “Notes”).

As part of the Tender Offer, Holly Energy is soliciting consents (the “Consent Solicitation”) from the holders of the Notes for certain proposed amendments that would eliminate or modify certain covenants and events of default and other provisions contained in the indenture governing the Notes. Holders who tender their Notes will be deemed to consent to the proposed amendments and holders may not deliver consents to the proposed amendments without tendering their Notes in the Tender Offer. The Tender Offer and Consent Solicitation are being made pursuant to the Offer to Purchase and Consent Solicitation Statement, dated February 27, 2012 (the “Offer to Purchase”), and a related Consent and Letter of Transmittal, which more fully set forth the terms and conditions of the Tender Offer and Consent Solicitation.

The Tender Offer will expire at midnight, New York City Time, on March 23, 2012, unless the Tender Offer is extended or earlier terminated (the “Expiration Date”). Under the terms of the Tender Offer, holders of the Notes who validly tender and do not withdraw their Notes prior to midnight, New York City Time, on March 9, 2012 (as such time and date may be extended, the “Consent Payment Deadline”) and whose notes are accepted for purchase, will receive the “Total Consideration,” which is equal to (i) $983.00 per $1,000.00 in principal amount of Notes validly tendered (the “Tender Offer Consideration”) plus (ii) a consent payment of $30.00 per $1,000.00 in principal amount of the Notes validly tendered (the “Consent Payment”). Holders of Notes who validly tender their Notes after the Consent Payment Deadline but on or before the Expiration Date, and whose notes are accepted for purchase, will receive only the Tender Offer Consideration.

Holly Energy reserves the right but is under no obligation, at any point following the Consent Payment Deadline and before the Expiration Date, to accept for purchase any Notes validly tendered and not subsequently withdrawn at or prior to the Consent Payment Deadline (the “Early Settlement Date”). The Early Settlement Date will be determined at Holly Energy’s option and is currently expected to occur on March 12, 2012, subject to all conditions to the Tender Offer having been satisfied or waived by Holly Energy. In addition to the Total Consideration or the Tender Offer Consideration, holders whose Notes are accepted in the Tender Offer will receive accrued and unpaid interest from and including the most recent interest payment date, and up to, but excluding, the applicable settlement date. The final settlement date is expected to occur on the first business day following the Expiration Date, subject to all conditions to the Tender Offer having been satisfied or waived by Holly Energy.

Holly Energy expects to call for redemption any Notes not tendered in the Tender Offer and Consent Solicitation.

The Tender Offer and Consent Solicitation are contingent upon the satisfaction of certain conditions, including the condition that Holly Energy has completed one or more financing transactions on terms reasonably satisfactory to Holly Energy resulting in net proceeds to Holly Energy sufficient to pay the Total Consideration, plus the applicable interest payment described above, in respect of all the Notes. If any of the conditions are not satisfied, Holly Energy is not obligated to accept for payment, purchase or pay for, and may delay the acceptance for payment of, any tendered Notes and may even terminate the Tender Offer and Consent Solicitation. Full details of the terms and conditions of the Tender Offer and Consent Solicitation are included in the Offer to Purchase. Holly Energy’s results of operations could be impacted by fees, expenses and charges related to the Tender Offer and Consent Solicitation and the financing transactions described above.

This press release does not constitute a notice of redemption under the optional redemption provisions of the indenture governing the Notes, nor does it constitute an offer to sell, or a solicitation of an offer to buy, any security. No offer, solicitation, or sale will be made in any jurisdiction in which such an offer, solicitation, or sale would be unlawful.

Requests for documents relating to the Tender Offer and Consent Solicitation may be directed to Global Bondholder Services Corp., the Information Agent, at (866) 540-1500 or (212) 430-3774 (banks and brokers). Citigroup will act as Dealer Manager and Solicitation Agent for the Tender Offer and Consent Solicitation. Questions regarding the Tender Offer and Consent Solicitation may be directed to Citigroup at (800) 558-3745 (toll free) or (212) 723-6106 (collect).

About Holly Energy Partners, L.P. and Holly Energy Finance Corp.:

Holly Energy Partners, L.P., (“HEP”) headquartered in Dallas, Texas, provides petroleum product and crude oil transportation, terminalling, storage and throughput services to the petroleum industry, including HollyFrontier Corporation subsidiaries. HEP owns and operates petroleum product and crude gathering pipelines, tankage and terminals in Texas, New Mexico, Arizona, Washington, Idaho, Oklahoma, Utah, Wyoming and Kansas. In addition, HEP owns a 25% interest in SLC Pipeline LLC, a 95-mile intrastate pipeline system serving refineries in the Salt Lake City, Utah area.

Holly Energy Finance Corp. is a wholly-owned subsidiary of HEP, which was organized for the sole purpose of co-issuing the Notes and other debt securities of HEP. Holly Energy Finance Corp. does not have any operations of any kind and will not have any revenue other than as may be incidental to its activities as a co-issuer of the Notes and such other debt securities.

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All statements, other than statements of historical fact, included in this press release are forward-looking statements, including, but not limited to, statements identified by the words “anticipate”, “project”, “expect”, “plan”, “goal”, “forecast”, “intend”, “could”, “believe”, “may” and similar expressions and statements regarding our business strategy, plans and objectives for future operations. These statements reflect our current views with respect to future events, based on what we believe are reasonable assumptions. Certain factors could cause actual results to differ materially from results anticipated in the forward-looking statements. These factors include, but are not limited to: risks and uncertainties with respect to the actual quantities of petroleum products and crude oil shipped on our pipelines and/or terminalled, stored or throughput in HEP’s terminals and tanks; the economic viability of HollyFrontier Corporation, Alon USA, Inc. and HEP’s other customers; the demand for refined petroleum products in markets HEP serves; HEP’s ability to successfully purchase and integrate additional operations in the future; HEP’s ability to complete previously announced or contemplated acquisitions; the availability and cost of additional debt and equity financing; the possibility of reductions in production or shutdowns at refineries utilizing HEP’s pipeline, terminal and tankage facilities; the effects of current and future government regulations and policies; HEP’s operational efficiency in carrying out routine operations and capital construction projects; the possibility of terrorist attacks and the consequences of any such attacks; our ability to consummate the Tender Offer and Consent Solicitation; the impact of fees, expenses and charges related to the financing transactions described in this press release on HEP’s results of operations; general economic conditions; and other financial, operations and legal risks and uncertainties detailed from time to time in HEP’s Securities and Exchange Commission filings. Other factors described herein, or factors that are unknown or unpredictable, could also have a material adverse effect on future results. Please read “Risk Factors” in Item 1A of our Annual Report on Form 10-K for the year ended December 31, 2011. Except as required by securities laws, we do not intend to update these forward-looking statements and information.

FOR FURTHER INFORMATION, Contact:

Bruce R. Shaw, Senior Vice President and Chief Financial Officer

M. Neale Hickerson, Vice President, Investor Relations

Holly Energy Partners, L.P.

214/871.3555

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