The family of George Stinney hopes the court hearing will show he is innocent.
The motion says Stinney was convicted on a shaky confession in a segregated society that wanted revenge on a black boy accused of beating to death two white girls, ages 11 and 7 in Clarendon County.
The request includes sworn statements from two of Stinney's siblings, saying he was around them all day the girls were killed.
Stinney was executed 84 days after the girls disappeared.
Records of Stinney's confession and other evidence from the trial have disappeared.