Thibault was drafted by the Quebec Nordiques 10th overall in the 1993 NHL Entry Draft. He went on to play for the Nordiques, staying on for a short time after they moved to Denver and became the Colorado Avalanche. In 1995, midway through the Avalanche's first season in Denver, he was traded to the Montreal Canadiens in the trade that moved Patrick Roy to the Avalanche. Thibault played three seasons with the Canadiens before being traded to the Chicago Blackhawks in November 1998.