Barnaby was drafted 83rd overall in the
1992 NHL draft by the
Buffalo Sabres. He was assigned to the Victoriaville Tigres in the
Quebec Major Junior Hockey League for nearly a full season before he was called up to make his NHL debut with the Sabres in 1993. Barnaby continued with the Sabres until March 11,
1999, when he was traded to the
Pittsburgh Penguins. After just over a season with the Penguins, he was sent first to the
Tampa Bay Lightning on February 1,
2001, then to the
New York Rangers on
December 12, 2001. Barnaby continued with the Rangers until
March 8,
2004, when they sent him to the
Colorado Avalanche. He played only 13 games with the Avalanche, then signed with the
Chicago Blackhawks on
July 2, 2004. Barnaby's final move came in
2006, when he signed with the
Dallas Stars for his final NHL season.