Rex Allen Beckworth is charged with capital murder along with his stepbrother, James Earl Walker.
Prosecutors are trying to prove the suspects shot 87-year-old Bessie Lee Thweet at point-blank range in January of 2000.
Walker was arrested in Summer 2000, but Beckworth was a fugitive until he was picked up in Phoenix, Arizona, six months later.
Jury selection begins Thursday.
Court officials hope to hear opening arguments in the case Friday, and a verdict should be reached by the middle of next week.
Beckworth is being held without bond in the Houston County Jail.
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