Exhibit 99.1

TEL OFFSHORE TRUST

THE BANK OF NEW YORK MELLON TRUST COMPANY, N.A., CORPORATE TRUSTEE 919 CONGRESS AVENUE / AUSTIN, TEXAS 78701 / (800) 852-1422

TEL OFFSHORE TRUST ANNOUNCES AUCTION PROCESS FOR SALE OF ROYALTY INTEREST

AUSTIN, TEXAS AUGUST 5, 2011—TEL OFFSHORE TRUST (the “Trust”) announced that Chevron U.S.A. Inc. (“Chevron”), as the managing general partner of the TEL Offshore Trust Partnership (the “Partnership”), has commenced a formal auction process for the sale by the Partnership of its overriding royalty interest, or “Royalty”, equivalent to a 25% net profits interest, in certain oil and gas properties located offshore Louisiana (the “Royalty Properties”).  The principal asset of the Trust consists of a 99.99% interest in the Partnership.  In turn, the principal asset of the Partnership is the Royalty.  The Trust’s source of capital is the Trust’s share of the net proceeds from the Royalty Properties under the terms of the Royalty.

Chevron has engaged EnergyNet.com, Inc. to conduct the marketing process and the related auction for the Royalty, with the bids in the auction currently scheduled to be due on Tuesday, August 30, 2011.  EnergyNet.com, Inc. is a FINRA-registered broker dealer that provides marketing services to the oil and gas industry.  Potential bidders should contact EnergyNet.com, Inc. (by going to www.energynet.com or by calling Toll Free at (877) 351-4488) for further details regarding the process.  The entire Royalty is being marketed for sale; however, the Partnership has reserved the right to sell all or only a portion of its interest in the Royalty.

On October 7, 2008, the Trust announced that production from the two most significant Royalty Properties had ceased following damage inflicted by Hurricane Ike in September 2008.  The Trust has not received a distribution associated with net proceeds from the Royalty since December 2008.  Consequently, the Trust has not been able to make a distribution to holders of Trust units for ten consecutive quarters, or since January 9, 2009.  Production at Ship Shoal 182/183 recommenced in the second half of 2009.  The platforms and wells on Eugene Island 339 were completely destroyed by Hurricane Ike, and Chevron is completing the plugging and abandonment of such wells.  Chevron is in the process of redeveloping Eugene Island 339, and has entered into a participation agreement with a third party to assist in such redevelopment; however, there is no obligation for Chevron to continue to pursue such redevelopment.

Total future net revenues attributable to the Partnership’s interest in the Royalty were estimated at $19.8 million as of October 31, 2010.  However, there are not likely to be distributable net proceeds from the Royalty Properties for the foreseeable future.  Because of the lack of receipt of net proceeds, the Trust does not currently have sufficient cash flow to pay expenses on a current basis.

In March 11, 2011, the trustees of the Trust provided written notice to Chevron that, pursuant to the Trust’s trust agreement, the Trust needed funds to pay for liabilities of the Trust and that the trustees therefore instructed Chevron, as the managing general partner of the Partnership, to sell such portion, and only such portion, of the Royalty that would provide the Trust with a current distribution equal to

$2,000,000 from the proceeds of such sale.  Based on a recommendation from Chevron, as the managing general partner of the Partnership, Chevron is marketing for sale by the Partnership the entire Royalty, while reserving the right to sell only a portion of the Royalty.  The trustees of the Trust are in ongoing discussions with Chevron regarding the sales process conducted by Chevron and EnergyNet.com, Inc.  In notices to Chevron, the trustees of the Trust have reserved the right to withdraw, at any time, the instruction to sell interests in the Royalty.  There can be no assurance that a sale of interests in the Royalty will be consummated, or as to the terms, conditions and timing of such a sale of interests in the Royalty.

Pursuant to the terms of the Trust’s trust agreement, the trustees of the Trust, on behalf of the Trust, are authorized to borrow funds, and pledge the assets of the Trust to secure payments of such borrowings, in the event that cash on hand is not sufficient to pay the liabilities of the Trust.  The trustees are continuing to seek a loan to the Trust to be able to pay liabilities of the Trust.  However, there can be no assurance that such a loan will be obtained, or as to the terms, conditions and timing of such a loan.

This press release contains forward-looking statements.  Although the managing general partner of the TEL Offshore Trust Partnership has advised the Trust that the managing general partner believes that the expectations contained in this press release are reasonable, no assurances can be given that such expectations will prove to be correct.  The Working Interest Owners of the Royalty Properties alone control historical operating data, and handle receipt and payment of funds relating to the Royalty Properties and payments to the Partnership for the related Royalty.  The trustees of the Trust cannot assure that errors or adjustments by such Working Interest Owners, whether historical or future, will not affect future royalty income and distributions by the Trust.  Other important factors that could cause these statements to differ materially include delays and costs in connection with repairs or replacements of hurricane-damaged facilities and pipelines, including third-party transportation systems, the timing of capital expenditures, if any, the actual results of drilling operations, risks inherent in drilling and production of oil and gas properties, the valuation, terms and conditions of any potential sales of the Royalty and Royalty Properties, and other factors described in the Trust’s Form 10-K for 2009 under “Item 1A. Risk Factors” and in the Trust’s Form 10-Q for the quarterly period ended March 31, 2011 under “Part II, Item 1A. Risk Factors”.  Statements made in this press release are qualified by the cautionary statements made in these risk factors.  The Trust does not intend, and assumes no obligations, to update any of the statements included in this press release.

The Bank of New York Mellon Trust Company, N.A.

AS CORPORATE TRUSTEE

CONTACT:  Mike Ulrich

(800) 852-1422

www.businesswire.com/cnn/tel-offshore.htm

2