He played for the Edmonton Eskimos, Calgary Stampeders, and Saskatchewan Roughriders of the CFL, and the Dallas Cowboys and Cincinnati Bengals of the NFL.

Chevrier attended McGill University, where he was a teammate of future NFL player Jean-Philippe Darche.

As a freshman in 1996, He started seven games at "rush" end and nose guard, collecting 24 tackles (three for loss), one sack and one fumble recovery.

As a second year student in 1997, he started 7 games at "rush" end, making 27 tackles (two for loss), two sacks and one fumble recovery.

As a fifth year student in 2000, he started eight games at strongside defensive tackle and handled deep snapping duties.

He took part in the East–West Shrine Game, recovering in six weeks following a stabbing as a bouncer at a bar in which he suffered a punctured lung.

Chevrier was selected by the Jacksonville Jaguars in the seventh round (241st overall) of the 2001 NFL draft to play as a long snapper.

On September 4, 2001, Chevrier was claimed off waivers by the Dallas Cowboys, who were looking to replace long snapper Dale Hellestrae who was released in a salary-cap move.

[3] On November 13, he was cut after struggling with his long snapper duties and having an errant snap that led to placekicker Tim Seder being injured.

On September 26, 2002, he signed with the Edmonton Eskimos of the Canadian Football League, playing in five games and making four tackles.

In 2010, he posted five special teams tackles, one punt for 53 yards, one fumble recovery and one reception for his second career touchdown.