Libya: bomb wounds soldier at Benghazi checkpoint
His body was found at Rough Creek Lodge range on Saturday with that of another man. A suspect was arrested.
Mr Kyle, 38, wrote the 2012 bestseller American Sniper, about the psychology of a sniper, in which he said that he had killed more than 250 people.
He served four tours of duty in Iraq and was decorated for bravery.
The gunman opened fire at about 15:30 local time (21:30 GMT) then fled in a pick-up truck belonging to one of the victims, local media reported.
Erath County Sheriff Tommy Bryant said the motive for the killings was unclear, and was unable to explain how the two men were shot.
But he said a 25-year-old suspect was detained five hours later more than 70 miles (110 km) from the scene.
Scott McEwen, who co-authored the book with Kyle, said: "It just comes as a shock and it's staggering to think that after all Chris has been through, that this is how he meets his end, because there are so many ways he could have been killed."
BBC
