What part of that are you not understanding?Subparagraph (A) shall not apply to the possession of a firearm--
`(i) on private property not part of school grounds;
`(ii) if the individual possessing the firearm is licensed to do so by the State in which the school zone is located or a political subdivision of the State, and the law of the State or political subdivision requires that, before an individual obtain such a license, the law enforcement authorities of the State or political subdivision verify that the individual is qualified under law to receive the license;
"Shall not apply"... "if the individual possessing the firearm is licensed"
Looks clearly to me that your Texas CHL covers you... well, unless you go to school zones outside of Texas.