The Skull by Philip K. Dick, Science Fiction, Adventure in Bloomington, MN

Conger, the protagonist, is given a chance to get out of jail if he agrees to travel back in time and kill a man.
He has agreed to kill a stranger he has never seen. He isn't concerned about getting the wrong man. He knows what the man looked like. There was no way he could make a mistake about his target's identity -- he has the man's skull under his shoulder.