LeClair was drafted by the Montreal Canadiens with the 33rd pick in the 1987 NHL Entry Draft after graduating from Bellows Free Academy (B.F.A.) High School in St. Albans, Vermont. One of the most highly recruited hockey players in New England, LeClair put his NHL aspirations on hold to attend the University of Vermont on a full scholarship. His fans didn't have to wait long to see him score in his first collegiate game. After the final game of his senior year he signed with the Canadiens and, less than a week later, played and scored in his first NHL game. As a member of the Canadiens, LeClair was on the Stanley Cup-winning team in 1993, where he scored two overtime game-winning goals during the 1993 Stanley Cup Finals.