Jury selection began Monday in an Ector County courtroom for the trial of James Doyle Burwell.
Burwell, 28, is charged with 3 counts of capital murder.
Burwell is accused of killing Dick and Peggy Glover early on the morning of May 23, 2011.
The murder reportedly happened during a robbery at the elderly couple's home in the 2700 block of Fair Oaks Circle in Odessa.
Law enforcement officials later arrested Burwell in Lubbock.
Burwell was reportedly driving the Glovers' 2007 Lincoln Navigator at the time of his arrest, and Odessa Police say he had one of Peggy Glover's credit cards on him.
Burwell also reportedly had bloody boots on at the time of his arrest.
Peggy Glover, 74, was the owner and CEO of Gemstar Fabrication. Dick Glover, 76, was the owner of the Dick Glover Company, which specializes in oil field supplies.
The Ector County District Attoney's Office decided to waive the death penalty for Burwell at the request of the Glovers' children.
If he's convicted, Burwell faces a mandatory sentence of life in prison without parole.
Meanwhile, a relative of Burwell's -- Tisha Burwell -- was arrested on October 11th and accused of tampering with evidence to be used in the capital murder trial.
Tisha Burwell is now charged with tampering with or fabricating physical evidence.