Born in Montreal, Chiasson's road to the NHL began when he left Quebec as a high school senior to attend Northwood High in Lake Placid, N.Y., and play hockey in the 2007-08 season.

He spent 2008-2009 with Des Moines of the United States Hockey League, where he was coached by former NHL forward J.P. Parise, and had 50 points in 56 games. That convinced the Dallas Stars to selected Chiasson in the second round (No. 38) of the 2009 NHL Draft.

To further his hockey education, Chiasson enrolled at Boston University, which was the defending NCAA champion, and spent three years as part of the Terriers' powerhouse program. After the 2011-2012 season at BU, having led the Terriers with 46 points, Chiasson signed with Dallas and was assigned to Texas of the American Hockey League, where he played nine games that season.

He started the 2012-13 season with Texas and played 57 games before being called up to the Stars. He made a great first impression, with six goals and seven points in seven games.

With the Stars for a full season in 2013-14, he had 13 goals and 35 points in 79 games, but in the summer was traded to the Ottawa Senators for Jason Spezza.

Chiasson had 19 goals and 40 points over two full seasons in Ottawa before being traded to the Flames on June 27, 2016.