Exhibit 99.1

TEL OFFSHORE TRUST

THE BANK OF NEW YORK MELLON TRUST COMPANY, N.A., CORPORATE TRUSTEE

919 CONGRESS AVENUE / (800) 852-1422 / AUSTIN, TEXAS 78701

TEL OFFSHORE TRUST ANNOUNCES THERE WILL BE NO THIRD QUARTER 2011 DISTRIBUTION

AUSTIN, TEXAS SEPTEMBER 30, 2011—TEL OFFSHORE TRUST announced that there will be no trust distribution for the third quarter of 2011 for unitholders of record on September 30, 2011. The Trust has not been able to make a distribution to unitholders for eleven consecutive quarters, or since January 9, 2009. The financial and operating information included herein for the Trust’s third quarter of 2011 reflects financial and operating information with respect to the royalty properties for the months of May, June and July 2011.

Gas revenues recorded by Chevron U.S.A. Inc. (“Chevron”), as a Working Interest Owner, on its royalty properties decreased approximately 25% to $132,665 in the third quarter of 2011 from $177,689 in the second quarter of 2011.  Natural gas volumes during the third quarter of 2011 decreased approximately 37% to 27,692 Mcf from 44,061 Mcf during the second quarter of 2011. The decrease in volumes is due primarily to normal fluctuation in production and a prior period adjustment. The average price received for natural gas increased approximately 19% to $4.79 per Mcf in the third quarter of 2011 as compared to $4.03 per Mcf received in the second quarter of 2011.

Crude oil revenues recorded by Chevron, as a Working Interest Owner, on its royalty properties increased approximately 16% to $5,082,567 in the third quarter of 2011 from $4,398,969 in the second quarter of 2011. Oil volumes during the third quarter of 2011 increased approximately 3% to 43,221 barrels, compared to 42,109 barrels of oil produced in the second quarter of 2011. The average price received for oil increased approximately 13% to $117.59 per barrel in the third quarter of 2011 as compared to $104.47 per barrel received in the second quarter of 2011.

The Trust’s share of capital expenditures increased by $222,696 in the third quarter of 2011 to $326,427, as compared to $103,370 in the second quarter of 2011. The increase in capital expenditures is due primarily to facility improvement projects at Ship Shoal 182/183. The Trust’s share of operating expenses increased by $1,421,555 in the second  quarter of 2011 to $6,323,709 as compared to $4,902,153 for the second quarter of 2011. The increase in operating expenses is due primarily to increased well and platform abandonment costs at Eugene Island 339 and workover expenses at Ship Shoal 182/183. Chevron has informed the Trust that the estimate of the Trust’s net portion of the aggregate cost to plug and abandon the wells subject to the overriding royalty interest on Eugene Island 339 has increased from approximately $15 million to approximately $16.5 million, approximately $14.2 million of which had been incurred through July 31, 2011.

For the third quarter of 2011, under the terms of the conveyance for the royalty properties, production costs for the royalty properties exceeded gross proceeds thereof, with the Trust’s portion of such excess equal to approximately $450,000. As of July 31, 2011, aggregate development and production costs for

the royalty properties since November 2008 have exceeded the related proceeds of production from the royalty properties by approximately $4.2 million, net to the royalty interest.  As a result, the Trust will not be receiving any net proceeds for the third quarter of 2011.  In the fourth quarter of 2010, Chevron U.S.A., Inc. withdrew $4,304,894 from the Special Cost Escrow account of the Working Interest Owners (a reserve fund for certain costs) to cover expenses incurred in connection with the plugging and abandonment of Eugene Island 339, which served to reduce the amount by which development and production costs exceeded the related proceeds from production; however, additional deposits to the Special Cost Escrow account will be required in future periods in accordance with the terms of the underlying conveyance of the royalty if, and when, net proceeds would otherwise be payable on the royalty.  In the third quarter of 2011, no dollars were escrowed or released from the Special Cost Escrow account of the Working Interest Owners, leaving a balance of $1,000 in the Special Cost Escrow account.

As previously reported, Chevron, as the Managing General Partner of the TEL Offshore Trust Partnership, has been marketing for sale by the Partnership its overriding royalty interest (a 25% net profits interest in certain oil and gas properties), as the Trust needs funds to pay for liabilities of the Trust. The Partnership reserved the right to sell only a portion of the royalty interest. Bids were due on August 30, 2011 and the Partnership is continuing negotiations regarding a potential sale. There can be no assurance that such a sale will be consummated, or the terms, conditions and timing of any such sale.

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 alone control historical operating data, and handle receipt and payment of funds relating to the royalty properties and payments to the Trust for the related royalty. The Trustees of the Trust cannot assure that errors or adjustments by the 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 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 other factors described in the Trust’s Form 10-K for 2010 under “Item 1A. Risk Factors” and in the Trust’s Form 10-Q for the quarterly period ended June 30, 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

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