Yes, Texas law allows it and PC 1.08 states that "no lower level of government may pass a law that penalizes any conduct which is specifically covered by the State statutes;" but some cities such as San Antonio and Port Arthur have still passed illegal ordnances that violate the state law. As long as you keep the firearm concealed, you won't have any problems; but if for any reason you are caught it could be an expensive adventure in the court system to clear yourself!
Of course, then you can sue the city for your expenses and then some!