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 FOURTH QUARTER 2010 DISTRIBUTION; INTENTION TO DELIST UNITS FROM NASDAQ

AUSTIN, TEXAS DECEMBER 21, 2010—TEL OFFSHORE TRUST announced that there will be no trust distribution for the fourth quarter of 2010 for unitholders of record on December 31, 2010. The Trust has not been able to make a distribution to unitholders for eight consecutive quarters, or since January 9, 2009. The financial and operating information included herein for the Trust’s fourth quarter of 2010 reflects financial and operating information with respect to the royalty properties for the months of August, September and October 2010.

Gas revenues recorded by the Working Interest Owners on the royalty properties increased approximately 82% to $434,071 in the fourth quarter of 2010 from $239,020 in the third quarter of 2010.  Natural gas volumes during the fourth quarter of 2010 increased approximately 60% to 84,237 Mcf from 52,524 Mcf during the third quarter of 2010. The increase in volumes is due primarily to increased production at Ship Shoal 182/183 and a 15,055 Mcf prior period adjustment related to volume allocations at Eugene Island 339.  The average price received for natural gas increased approximately 13% to $5.15 per Mcf in the fourth quarter of 2010 as compared to $4.55 per Mcf received in the third quarter of 2010.

Crude oil revenues recorded by the Working Interest Owners on the royalty properties increased approximately 4% to $3,553,883 in the fourth quarter of 2010 from $3,420,890 in the third quarter of 2010. Oil volumes during the third quarter of 2010 increased approximately 6% to 45,399 barrels, compared to 42,811 barrels of oil produced in the third quarter of 2010. The increase in volumes is due primarily to increased production at Ship Shoal 182/183. The average price received for oil decreased approximately 2% to $78.28 per barrel in the fourth quarter of 2010 as compared to $79.91 per barrel received in the third quarter of 2010.

The Trust’s share of capital expenditures increased by $931,620 in the fourth quarter of 2010 to $1,117,404, as compared to $185,785 in the third quarter of 2010. The increase in capital expenditures is due primarily to platform upgrades and repairs and fuel gas meter upgrades at Ship Shoal 182/183.  The Trust’s share of operating expenses increased by $1,765,079 in the fourth quarter of 2010 to $8,559,670 as compared to $6,794,591 for the third quarter of 2010. The increase in operating expenditures is due primarily to an increase in the amount of abandonment work done at Eugene Island 339 in the fourth quarter as compared to the third quarter. Completion of abandonment work at Eugene Island is not expected until the second quarter of 2012.

For the fourth quarter of 2010, 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 $1,511,000. As of October 31, 2010, 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 $7.85 million, net to the royalty interest. As a result, the Trust will not

be receiving any net proceeds for the fourth quarter of 2010.  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, leaving a balance of $1,000 in the Special Cost Escrow account.  After taking into account such withdrawal, aggregate development and production costs in excess of the related proceeds for the royalty properties is approximately $3.55 million, net to the royalty interest; however, additional deposits to the Special Cost Escrow account would be required in future periods in accordance with the underlying conveyance of the royalty if, and when, net proceeds would otherwise be payable on the royalty.

In November 2010, Chevron, as the operator of Eugene Island 339, submitted to the Bureau of Ocean Energy Management, Regulation and Enforcement, or BOEM, a new request to seek a Suspension of Operations, or SOP, in order to proceed with the redevelopment of Eugene Island 338 and 339. The prior SOP expired on November 30, 2010.  The new request contemplates an activity schedule consistent with the initial SOP.  A response from the BOEM, which could affect the activity schedule, is not expected until some time in 2011.  There is no obligation for Chevron to continue to pursue the redevelopment.  At this time, there can be no assurance that the Chevron request for an SOP will be granted by the BOEM or as to the ultimate outcome of any such redevelopment, or the timing or costs associated therewith.

In an effort to reduce expenses, the trustees of the Trust have determined that it is in the best interest of the Trust to voluntarily delist the units of beneficial interest in the Trust, or Units, and to cause the Units to no longer be traded on the NASDAQ.  The Trust plans to file a Form 25 with the Securities and Exchange Commission on or about December 31, 2010 and expects that the Form 25 will become effective on or about January 10, 2011.

On October 7, 2008, the Trust announced that production from the two most significant oil and gas properties associated with the Trust had ceased following damage inflicted by Hurricane Ike in September 2008.  As a result of the damage inflicted by Hurricane Ike, the Trust has not received a distribution of net proceeds from Chevron with respect to the royalty since December 2008, and positive net proceeds from the royalty properties are not likely for the foreseeable future.  The Trust continues to utilize its cash reserves to pay expenses; however, as of September 30, 2010, those reserves were approximately 67% of the average annual expenses of the Trust during the three-year period ended September 30, 2010.

The decision to voluntarily delist from the NASDAQ is based primarily on the Trust’s desire to conserve its cash reserves, and its recognition that the benefits of maintaining NASDAQ listing have declined.  The trading volume and price of the Units have been limited, and the Trust believes that the benefits of listing do not justify the expense, compliance requirements and administrative burdens of maintaining NASDAQ listing.  As a result of the voluntarily delisting, the Trust will realize annual cost savings of $27,500 in annual fees required by the NASDAQ.

The Trust has not arranged for the Units to be listed or registered on another national securities exchange or for the quotation of the Units in a quotation medium.  There can be no assurance as to whether, and to what extent, a trading market will develop by any market makers for the Units.  Following the voluntarily delisting of the Units from NASDAQ, the Trust intends to continue to file reports pursuant to the requirements of the Securities Exchange Act of 1934, as amended.

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

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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 2009 under “Item 1A. Risk Factors” and in the Trust’s Form 10-Q for the quarterly period ended September 30, 2010 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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