Zombie237,
"A person commits an offense of unlawfully carrying a
weapon if the person intentionally, knowingly, or recklessly
carries a handgun on or about his or her person
unless the
person is on one’s own premise or premises under the person’s
control or inside of or directly en route to a motor vehicle
that is owned by the person or under the person’s control.
It is unlawful to intentionally, knowingly or recklessly carry
on or about one’s person a handgun in a motor vehicle if the
handgun is in
plain view or the person is engaged in criminal
activity (other than a misdemeanor traffic violation), prohibited
by law from possessing a firearm or is a member of a street
gang."
http://www.nraila.org/statelawpdfs/TXSL.pdf
No where in the law does it say it must be out of reach, only that it must be concealed...assuming you're not in some kind of street gang or engaging in illegal activity.