Hennessy began his professional career with the San Jose Sharks' American Hockey League (AHL) affiliate, the Cleveland Barons, during the 2005–06. He led the Barons in goals (24) and assists (39) for 63 points in 80 games. He was one of only two players on the team to play in every regular-season game. Hennessy holds the franchise records for both goals and points in a season by a rookie and was named the Barons Rookie of the Year for the 2005–06 season.
