Antonio Chance is charged with killing Cynthia Moreland in Raleigh in August of 2006.
Prosecutors say he dumped her body in Harnett County.
Defense attorneys argue that Chance has an IQ below 70, which is the threshold for mental retardation.
State law bans the execution of mentally retarded convicts. It also requires they show they cannot function in society.
Wake County prosecutors say they are not convinced that is the case with Chance.