Career
Baun is the grandson of former Toronto Maple Leafs great Bobby Baun. After a Canadian minor junior league career with the Toronto Junior. Canadiens and the Cornwall Colts, Baun opted to pursue an collegiate career in committing with Colgate University of the ECAC conference.
Undrafted and upon completing his junior season in Colgate with 29 points in 38 games, earning an ECAC Third All-Star Team selection, Baun was signed to a two-year entry level contract with the Chicago Blackhawks of the National Hockey League on March 26, 2015.
He immediately joined the Blackhawks for the remainder of the 2014-2015 season, and later made his National Hockey League debut in a 2-1 defeat to the Minnesota Wild on April 7, 2015.