Chiasson was selected by the Dallas Stars in the second round, 38th overall, in the 2009 NHL Entry Draft and has earned 106 points (50g, 56a) in 320 career NHL games. He ranks 27th among players in the 2009 NHL Entry Draft class in career games played and 20th in career goals. In his rookie season with the Stars in 2013-14, Chiasson became the first player to score nine goals in his first 10 career games since Winnipeg Jets forward Teemu Selanne accomplished that feat in the 1992-93 season. One of 10 Dallas rookies to play in the 2013-14 season, Chiasson led all Stars rookies with 35 points and 22 assists, ranking seventh in points and tied for seventh in assists among the rookies in the NHL.
As a member of the Senators during the 2015-16 season, the Montreal, Que, native played in 77 games, registering 14 points (8g, 6a).
A three-year student at Boston University, Chiasson recorded 99 points (36g, 63a) in 108 games with the Terriers. Chiasson led Boston University in scoring in his sophomore and junior year. In his final two collegiate seasons, Chiasson was named as a Hockey East Honorable Mention All-Star.