Chevrier was not drafted by any NHL team after seeing limited duty in major junior hockey with the Cornwall Royals of the QMJHL in 1978-79. He was out of hockey for a short period of time before deciding to join Miami University of Ohio in 1982-83. He played 65 games in the NCAA over two seasons before looking for work as a professional. Chevrier was signed to a contract and played for the Fort Wayne Komets of the IHL, starting 56 games.

Just one year later, Chevrier found himself playing in 37 games with the New Jersey Devils. If that seemed hard to believe, he suited up for 58 and 45 games in the next two seasons. In 1988-89, Chevrier joined the Winnipeg Jets, and played in goal for 22 games before being traded to the Chicago Blackhawks where he played another 27 games. He returned to Chicago the next year, playing in 39 games, before being traded once again, this time to the Pittsburgh Penguins, where he dressed for three games.

Chevrier's NHL career ended in Detroit in 1990-91, where he donned the pads for three games while seeing the majority of his playing time with the IHL's San Diego Gulls. Following the 1990-91 season, Chevrier retired from the game.

Courtesy of the Hockey Hall of Fame