GC 411.172 Eligibility.
(1) Be a legal resident of this state; "no longer applies"
(2) at least 21 years of age;
(3) not convicted of a felony;
(4) not charged with the commission of a Class A or B misdemeanor or disorderly conduct or a felony;
(5) is not a fugitive from justice;
(6) is not a chemically dependent person;
(7) is not incapable of exercising sound judgment with respect to the proper use and storage of a handgun;
(8) has no convictions in the past 5 years of a Class A or B misdemeanor or disorderly conduct;
(9) is qualified under federal and state law to purchase a handgun;
(10) is not delinquent in making child support payment administered or collected by the attorney general;
(11) is not delinquent in the payment of a tax or other money collected by the comptroller, the tax collector of a political subdivision of the state, or any agency or subdivision of the state;
(12) is not under a court protective or restraining order affecting the spousal relationship;
(13) has not, in the 10 years preceding the date of application, been adjudicated as having engaged in delinquent conduct violating a penal law of the grade of felony.
(14) has not made any material misrepresentation, or failed to disclose any material fact, in an application submitted...
Note: The above is paraphrased - follow the link below for the full text.
You may download the complete Texas Handgun Laws and Statues
Form # LTC-16, "Current Laws" at the DPS website: