Jury selection is set for Thursday, and an Erath County court will begin sifting through 800 hundred potential jurors, the Stephenville Empire-Tribune reported.
An attorney for Routh wants the trial's venue moved, saying a fair trial is impossible there.
With a population of just under 40,000 people, the defense says it might be hard to find even a handful who:
A day at the range
Kyle, who claimed to be the deadliest sniper in U.S. history for his 160 confirmed kills in Iraq, had already risen to fame for his bestselling autobiography, "American Sniper,"
when he died on February 2, 2013.
Kyle had taken Routh and another man to a firing range.
Routh, an unemployed former Marine, was one of them. He suffered from severe PTSD. Kyle was doing charitable work to help former soldiers suffering from the psychological disorder.
The other man with them was Chad Littlefield, who was Kyle's friend.
It was a Saturday, and the three men arrived at the Rough Creek Lodge, about 90 miles southwest of Dallas after 3 p.m.
The range makes up a small, remote part of the sprawling 11,000-acre resort, and the men were isolated.
"So, there wasn't anybody anywhere close to that," Sheriff Tommy Bryant said back then. There were no witnesses to the killing of Kyle and Littlefield.
Less than two hours after they had arrived, a hunting guide passing by found the two victims motionless, went to the lodge and called 911. Kyle and Littlefield were dead when officers arrived.
Routh was gone, and so was Kyle's black Ford pickup. Law enforcement put out an all-points bulletin.
Police: Fleeing in Kyle's truck
Routh drove up in it at his sister's house 65 miles away, police said. She called 911.
"I'm terrified for my life," she said. Routh had told her that he killed two men.
"They went out to a shooting range. Like, he's all crazy," Routh's sister told authorities. "My husband is going to talk to you, because I'm so nervous."
Routh got back into the truck and hit the road again, police said. But he was easy to find. Officers caught up with him that evening at his home in a Dallas suburb.
While talking with police, he jumped back into the truck and sped off again, police say. They gave chase and stopped him after spiking his tires. He did not struggle when they arrested him, police said.
Routh's attorney has said his client will plead not guilty by reason of insanity.
Kyle learned to shoot on hunting trips with his father, then went on to serve four combat tours in Iraq with the SEALs, though his official biography notes he also worked with Army and Marine units.
He received two Silver Stars and other commendations before leaving the Navy in 2009 -- claiming that, in his years as a sniper, he'd killed more than 150 people, which he called a record for an American.
He said that while killing did not come easy at first, he knew it meant saving lives.
"The first time, you're not even sure you can do it," he said in the interview. "But I'm not over there looking at these people as people. I'm not wondering if he has a family. I'm just trying to keep my guys safe."
Kyle's story and the movie made from it have triggered broad enthusiasm but also drawn critics and doubts about his accounts.
Correction: Earlier versions of this report incorrectly described the military background of Chad Littlefield, who was killed with Chris Kyle. Littlefield was not a veteran.