The justices said Monday they will use the case of Hank Skinner to decide whether prison inmates may use a federal civil rights law to do DNA testing that was not performed prior to their conviction.
Federal appeals courts around the country have decided the issue differently. The high court previously blocked Skinner's execution while it considered his appeal.
Skinner, 47, faced lethal injection for the bludgeoning and strangling of his girlfriend, Twila Jean Busby, 40, and the stabbing of her two adult sons. The slayings occurred at their home in the Texas Panhandle town of Pampa on New Year's Eve in 1993.
He was arrested about three hours after the bodies were found. Police found him in a closet at the trailer home of a woman he knew. He was splattered with the blood of at least two of the victims.