Even though he never put up great offensive numbers and his skating was questioned, he was a first round pick (20th overall) of the New York Rangers in 1989.
Everywhere Rice went he was lauded as a tireless worker and as tough but smart. He charged up and down his wing like an angry bull, crashing through anyone who got in the way. He was particularly strong in the corner and in front of the net banging away at loose pucks.
But injuries would plague Rice throughout his career. When a player's bread and butter is robust, physical play he needs to stay healthy and score some goals to stay in the lineup. Rice had troubles with one or both of these problems throughout his NHL career.
The New York Rangers never gave Rice much of a chance, and understandably so. When the Edmonton Oilers insisted Rice be part of a package including Bernie Nicholls to be exchanged in the Mark Messier blockbuster deal, the Rangers had no choice. Though losing Messier was devastating, many hoped the Oilers had just acquired their new leader.
Rice struggled to make the Oilers lineup in his first two seasons with the organization. By 1993-94 he had a mini-breakthrough with 17 goals and 32 points in 63 games, but missed a good portion of the campaign with a broken hand.
Rice sat out for nearly half of the next season as Group 1 free agent unable to agree to terms with the Oilers. The issue was finally resolved when the Hartford Whalers signed him to an offer sheet contract which Edmonton passed on matching.
Rice would play four seasons with the Hartford Whalers, moving with the franchise to Caroline to become the Hurricanes in 1997. He served mostly as a bottom six winger, but did emerge with a quiet 21 goals in 1996-97.
Rice retired from pro hockey early at age 27. Rice played a number of seasons of senior hockey near Toronto, opening his own hockey academy and doing a season of broadcasting. He returned to Raleigh, North Carolina where he designed outdoor living spaces for clients.