Kobasew spent one season playing at Boston College, starring on a team which won the National Championship and was loaded with players headed to the NHL. At the NCAA Frozen Four, he was named Most Valuable Player for the tournament. Following the Eagles' win over North Dakota, he jumped to the professional ranks.

 

He was drafted by the Calgary Flames in the first round (14th overall) in the 2001 NHL Entry Draft. During the 2004-2005 NHL lockout, Kobasew played with the AHL Lowell Lock Monsters, and helped the team reach a number of franchise records. He was named as captain for the team, and scored 75 points in 79 games. He was also selected to play for the Canadian contingent at that year's All-Star game.

 

While playing for the team that drafted him, the Calgary Flames, Kobasew scored his first career hat trick against the Colorado Avalanche on January 24, 2006.

 

Kobasew and Andrew Ference were traded by the Flames to the Boston Bruins on February 10, 2007 in exchange for Brad Stuart and Wayne Primeau.