In 1984, Chelios made the Montreal Canadiens for good, distinguishing himself with his play. During his early days, he was known for his offensive abilities, and his teammates even called him "Soft Hands Chelios." He earned a trip to the National Hockey League All-Star Game and was named to the 1985 NHL All-Rookie Team. He scored 64 points in 74 games, a high total for a defenseman even in the high-scoring 1980s, and finished second to Mario Lemieux for the Calder Memorial Trophy. In the playoffs that year, he scored 10 points in 9 games, with a +17 plus/minus. Although he only played 41 games in the 1985–86 season, he won his first Stanley Cup, playing in front of Conn Smythe Trophy-winning goaltender Patrick Roy.