 The Galveston Division of the United States District Court for the Southern District of Texas , the first federal court in Texas , is based in Galveston and has jurisdiction over the counties of Galveston , Brazoria , Chambers and Matagorda . It is housed in the United States Post Office , Customs House and Court House federal building in downtown Galveston . The United States Postal Service operates several post offices in Galveston , including the Galveston Main Post Office and the Bob Lyons Post Office Station . In addition the post office has a contract postal unit at the Medical Branch Unit on the campus of the University of Texas Medical Branch and the West Galveston Contract Postal Unit , located on the west end of Galveston Island in the <unk> community of Jamaica Beach . 
