Murray was raised in the Bridgewater, Nova Scotia area and played junior hockey for the Sudbury Wolves of the OHL. Murray was a first round draft pick, 18th overall by the Bruins in the 1991 NHL Entry Draft. He spent four season with the Bruins before being traded to the Pittsburgh Penguins with Bryan Smolinski for Kevin Stevens and Shawn McEachern. Murray's stay with the Penguins only lasted a little over a year and was eventually on the move again, this time he was traded to Los Angeles Kings for Ed Olczyk. Murray enjoyed moderate success with the Kings, picking up some good numbers during his 5 year stay, but on October 24, 2001, Murray would once again find himself in a middle of a trade. Murray was traded back to the Boston Bruins with Jozef Stumpel for Jason Allison and Mikko Eloranta.

 

Murray enjoyed his greatest offensive season in 2002-03, scoring 92 points (44 goals and 48 assists) for the Bruins and earning a spot in the 2003 NHL All-Star Game.