The Ellis County Sheriff's Department said Roberto Costilla of Ennis was being held on $1 million bail in the slayings that took place Saturday night in Bardwell, The Dallas Morning News reported.
The victims were a woman and man found dead on the kitchen floor of a residence and a man who died at a Dallas hospital after being found wounded in a hallway of the home.
Their names hadn't been released, the newspaper said.
Costilla was identified by a witness and he was arrested by Texas state troopers following a brief chase.
A possible motive for the killings wasn't reported.