Exhibit 99.1

Individual Trustees

Gary C. Evans

Thomas H. Owen, Jr.

Jeffrey S. Swanson

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 FOURTH QUARTER 2011 DISTRIBUTION

AUSTIN, TEXAS DECEMBER 22, 2011—TEL OFFSHORE TRUST announced that there will be no trust distribution for the fourth quarter of 2011 for unitholders of record on December 30, 2011. The Trust has not been able to make a distribution to unitholders for twelve consecutive quarters, or since January 9, 2009. The financial and operating information included herein for the Trust’s fourth quarter of 2011 reflects financial and operating information with respect to the royalty properties for the months of August, September and October 2011.

Gas revenues recorded by Chevron U.S.A. Inc. (“Chevron”), as a Working Interest Owner, on its royalty properties increased approximately 127% to $300,759 in the fourth quarter of 2011 from $132,665 in the third quarter of 2011.  Natural gas volumes during the fourth quarter of 2011 increased approximately 138% to 65,978 Mcf from 27,692 Mcf during the third quarter of 2011. The average price received for natural gas decreased approximately 5% to $4.56 per Mcf in the fourth quarter of 2011 as compared to $4.79 per Mcf received in the third quarter of 2011.

Crude oil revenues recorded by Chevron, as a Working Interest Owner, on its royalty properties decreased approximately 22% to $3,967,295 in the fourth quarter of 2011 from $5,082,567 in the third quarter of 2011. Oil volumes during the fourth quarter of 2011 decreased approximately 18% to 35,469 barrels, compared to 43,221 barrels of oil produced in the third quarter of 2011. The decrease in oil volumes is due primarily to down time at Ship Shoal 182/183 due to Tropical Storm Lee. The average price received for oil decreased approximately 5% to $111.85 per barrel in the fourth quarter of 2011 as compared to $117.59 per barrel received in the third quarter of 2011.

Capital expenditures decreased by $64,107 in the fourth quarter of 2011 to $262,320, as compared to $326,427 in the third quarter of 2011. The decrease in capital expenditures is due primarily to fewer expenditures for facility improvement projects at Ship Shoal 182/183 during the fourth of 2011. Operating expenses increased by $4,004,468 in the fourth quarter of 2011 to $10,328,177 as compared to $6,323,709 for the third quarter of 2011. The increase in operating expenses is due primarily to increased well and platform abandonment costs at Eugene Island 339.  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 $16.5 million to approximately $17.6 million, approximately $16.5 million of which had been incurred through October 31, 2011.

For the fourth 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 portion of such excess attributable to the entire 25% royalty interest, equal to approximately $1,691,000. As of October 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 $5.9 million,

net to the entire 25% royalty interest.  As a result, the Trust will not be receiving any net proceeds for the fourth 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 fourth 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, consummated the sale by the Partnership of 20% of the Partnership’s overriding royalty interest (a 25% net profits interest in certain oil and gas properties), as the Trust needed funds to pay for liabilities of the Trust. The Partnership retained an 80% interest in the royalty interest.

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 September 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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