The only provision that might apply, that I could find, are:
Texas Agriculture Code:
"§ 143.033. Injury to Trespassing Animal
If a person whose fence is insufficient under this subchapter maims, wounds, or kills a head of cattle or a horse, mule, jack, or jennet, or procures the maiming, wounding, or killing of one of those animals, by any means, including a gun or a dog, the person is liable to the owner of the animal for damages. This section does not authorize a person to maim, wound, or kill any horse, mule, jack, jennet, or head of cattle of another person."
And that only applies if your LIVESTOCK (not chickens) were trespassing on the others property.
There are numerous provisions for dogs that kill fowl in the Texas Health and Safety Code, Chapter 822. A full copy of this Code can be found at:
http://www.capitol.state.tx.us/statutes/he/he082200toc.html