Exhibit 99.1

Mesa Offshore Trust Announces Delay in Final Liquidating Distribution Due to Arbitration Demand

MESA OFFSHORE TRUST

JPMorgan Chase Bank, N.A., Trustee

	*NEWS*
	*RELEASE*

For Immediate Release

Austin, Texas July 23, 2010 - Mesa Offshore Trust (OTC BB symbol: MOSH.OB) announced today that certain unitholders of the Trust have made a demand for arbitration (“Demand for Arbitration”) under the Final Settlement Agreement dated May 19, 2009. As a result of the Demand for Arbitration and potential expenses and related contingencies associated with the Demand for Arbitration and the resolution thereof, the Trustee has decided to withhold current funds held by the Trust as a reserve for these contingent expenses and to defer making any final liquidating distribution at this time.

The claimants contend that Pioneer should have sold and accepted an offer from some of the claimant’s to buy an inchoate overriding royalty interest in Brazos A-39, which constituted part of the Pioneer settlement interests and the interest of the Mesa Offshore Trust Partnership (the “Partnership”). The offer made for this interest was $125,000, which would represent approximately $0.0017 per unit. Such claimants did not offer to buy the interest in the public auction of this and other interests held in accordance with the Settlement Agreement. The Settlement Agreement set forth that if the public auction did not result in a sale of the properties, “Pioneer will have the absolute right, in its sole discretion, to cancel, extinguish, or otherwise dispose of all or part of such interests.” The Trustee has been informed by Pioneer that the Brazos A-39 lease reverted to the Mineral Management Service in early March 2010, 180 days after the Midway Well ceased production back in September 2009. In addition, as previously announced, the Mesa Offshore Royalty Trust Partnership was dissolved in June 2010.

The Trustee will continue to act as Trustee and exercise its powers for the purpose of liquidating and winding up the affairs of the Trust at its termination until its duties have been fully performed and the Trust estate is finally distributed. In accordance with the Trust Indenture, the Trustee will as promptly as possible distribute the remaining assets in the Trust estate (including settlement proceeds), after paying, satisfying and discharging all of the liabilities of the Trust, or, when necessary, setting up reserves in such amounts as the Trustee in its discretion deems appropriate for contingent liabilities.

As previously announced as part of the liquidation and termination of the Trust, the Trustee set February 22, 2010 as the record date for unit holders entitled to payments of any final liquidating distributions. Accordingly, the Trustee will make payment of any final liquidating distribution only to unitholders of record as of February 22, 2010.

Contact:	Mesa Offshore Trust
	JPMorgan Chase Bank, N.A., as Trustee
	Mike Ulrich
	1(800) 852-1422

www.businesswire.com/cnn/mosh.htm

919 Congress Avenue, Austin, TX 78701

MESA OFFSHORE TRUST 8-K