Galley was born in Montreal and grew up in Ottawa, but the defenseman called neither city home during a well-traveled NHL career that saw him play with six teams in 17 seasons.

Galley was selected by the Los Angeles Kings in the fifth round (No. 100) of the 1983 NHL Draft after he had 46 points (17 goals, 29 assists) as a sophomore for Bowling Green. He was even better in 1983-84, scoring 15 goals and 67 points in 44 games.

As a result, Galley made his NHL debut with the Kings in 1984-85, and he showed quickly that he belonged by getting 38 points (eight goals, 30 assists) as a rookie. He played parts of two more seasons with the Kings before he was traded to the Washington Capitals on Feb. 14, 1987.

After playing one full season in Washington, Galley signed with the Boston Bruins as a free agent in the summer of 1988. He helped them reach the Stanley Cup Final in 1990, getting six points (three goals, three assists) in 21 games, though the Bruins lost to the Edmonton Oilers in five games.

He was traded for the second time on Jan. 2, 1992, to the Philadelphia Flyers, with whom he enjoyed his best offensive seasons.

Galley scored an NHL career-high 13 goals and had 62 points in 1992-93, then had NHL career highs in assists (60) and points (70) in 1993-94, when he appeared in the NHL All-Star Game for the second time.

Despite his offensive success, Galley was traded by the Flyers to Buffalo Sabres on April 7, 1995. He remained productive offensively for two more seasons with Buffalo, including getting 54 points (10 goals, 44 assists) in 1995-96, before returning to Los Angeles for three seasons.

He retired after playing his final NHL season with the New York Islanders in 2000-01.

In 1,149 NHL games, Galley had 600 points (125 goals, 475 assists), and 30 points (seven goals, 23 assists) in 89 playoff games.