Answer:
The Texas Motorist Protection Act (HB 1815), effective as of September 1, 2007, permits any law-abiding Texas resident the legal right to carry a handgun inside their motor vehicle in Texas without a Handgun License to Carry or any other permit. As long as you are legally permitted to own a firearm and the vehicle belongs to you, then the answer is yes; you may have a gun, loaded or unloaded, in your vehicle in the state of Texas.
