Born in LaSalle, Quebec, Chychrun was drafted 37th overall in the 1984 NHL Entry Draft by the Philadelphia Flyers. He made his NHL debut in the 1986–87 season with the Flyers, and stayed with them until the 1990–91 season. He also spent time in the NHL with the Los Angeles Kings, Pittsburgh Penguins and Edmonton Oilers. He played 262 games over his NHL career. His name was engraved on the Stanley Cup in 1992 as a member of the Pittsburgh Penguins.