Drafted 68th overall in the 1988 NHL Entry Draft by the New York Rangers, Amonte is best known for his time as a scoring star with the Chicago Blackhawks and for representing the United States in international play. Amonte made his debut in the 1991 playoffs. He impressed as a rookie, scoring over 30 goals and placing third in the balloting for the Calder Memorial Trophy. He played three seasons with the Rangers, scoring 84 goals, before being traded to the Chicago Blackhawks with seven games to go in the 1993–94 season, the year the Rangers went on to win the Stanley Cup. He gained stardom in Chicago where he was initially reunited with former Thayer Academy teammate Jeremy Roenick, scoring at least 30 goals six times and at least 40 three times, including having a five-season-long streak in which he did not miss a single game.