After college, he was selected in the fifth round (57th pick overall) of the 1956 NFL Draft, and played with the New York Giants and Green Bay Packers. He played in the first two overtime games ever in the NFL, in 1958 with the Giants against the Baltimore Colts and again in 1965 when he kicked the winning field goal for the Packers against the same Colts in a Western Conference playoff game at Green Bay. Chandler's fourth-quarter field goal that tied the game at 10–10 stirred controversy, as many Baltimore players and fans thought he missed the kick to the right. Chandler was named the punter on the NFL 1960s All-Decade Team. He went to the Pro Bowl after the 1967 season.