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 SECOND QUARTER 2011 DISTRIBUTION

AUSTIN, TEXAS JUNE 28, 2011—TEL OFFSHORE TRUST announced that there will be no trust distribution for the second quarter of 2011 for unitholders of record on June 30, 2011. The Trust has not been able to make a distribution to unitholders for ten consecutive quarters, or since January 9, 2009. The financial and operating information included herein for the Trust’s second quarter of 2011 reflects financial and operating information with respect to the royalty properties for the months of February, March and April 2011.

Gas revenues recorded by the Working Interest Owners on the royalty properties increased approximately 6% to $177,689 in the second quarter of 2011 from $168,351 in the first quarter of 2011.  Natural gas volumes during the second quarter of 2011 increased approximately 4% to 44,061 Mcf from 42,427 Mcf during the first quarter of 2011. The increase in volumes is due primarily to production slowly returning after the shut-in of the platform at Ship Shoal 182/183 during November 2010 for a tank replacement. The average price received for natural gas increased approximately 2% to $4.03 per Mcf in the second quarter of 2011 as compared to $3.97 per Mcf received in the first quarter of 2011.

Crude oil revenues recorded by the Working Interest Owners on the royalty properties increased approximately 57% to $4,398,969 in the second quarter of 2011 from $2,807,095 in the first quarter of 2011. Oil volumes during the second quarter of 2011 increased approximately 29% to 42,109 barrels, compared to 32,520 barrels of oil produced in the first quarter of 2011. The increase in volumes is due primarily to production slowly returning after the shut-in of the platform at Ship Shoal 182/183 during November 2010 for a tank replacement. The average price received for oil increased approximately 21% to $104.47 per barrel in the second quarter of 2011 as compared to $86.32 per barrel received in the first quarter of 2011.

The Trust’s share of capital expenditures decreased by $458,775 in the second quarter of 2011 to $103,370, as compared to $562,505 in the first quarter of 2011.  The Trust’s share of operating expenses increased by $1,188,769 in the second  quarter of 2011 to $4,902,153 as compared to $3,713,384 for the first quarter of 2011. The increase in operating expenses is due primarily to increased well and platform abandonment costs at Eugene Island 339.

For the second 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 $180,000. As of April 30, 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 $3.7 million, after taking into account insurance proceeds received by Chevron U.S.A., Inc. and allocated to Eugene Island 339, net to the royalty interest.  As a result, the Trust will not be receiving any net proceeds for the second 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 second 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 U.S.A, Inc., as the Managing General Partner of the TEL Offshore Trust Partnership, has been requested by the Trustees of the Trust to take certain actions involving a sale by the Partnership with respect to 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. Chevron is proceeding with a marketing process for sale by the Partnership of the overriding royalty interest. The Partnership reserves the right to sell only a portion of the royalty interest. There can be no assurance that such a sale can be consummated, or that the terms, conditions and timing of such a sale will be acceptable to the Partnership.

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, 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 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

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