Bollig agreed to a three-year contract extension in March. He had seven goals and seven assists while playing in 82 games this season, and then had an assist in 15 playoff games.
The Blackhawks used the draft pick, No. 83 overall, to take forward Matheson Iacopelli. The right wing had 41 goals and 23 assists last season for Muskegon of the USHL.
The 27-year-old Bollig has 201 penalty minutes in 125 career games with Chicago over three seasons.