Specifically, it is believed that the heir is Tom Riddle, who later becomes Lord Voldemort. This is revealed throughout the book "Harry Potter and the Chamber of Secrets" as Harry investigates the attacks on Muggle-born students.
However, the term "heir of Slytherin" is also a bit of a misnomer. While Tom Riddle is indeed descended from Salazar Slytherin, the true "heir" is actually a basilisk, the monster that was released by Tom Riddle from the Chamber.