Flight Instructor reported an NMAC during departure climb from DPA when an aircraft departing the parallel runway flew directly overhead them. Reportedly; ATC was not aware of the conflict.

Narrative

While flying in left closed traffic; using Runway 20L; another aircraft which departed the parallel; (20R) flew directly over us while our aircraft was in left crosswind at about 100-200 ft.Both aircraft were directed to depart their respected runway and our aircraft was told to remain in left closed traffic. The other aircraft was directed to depart and fly southbound on course departing the airport.On departure; our aircraft was at 1600 ft MSL on a left crosswind when a shadow briefly appeared and the other aircraft's engine was heard. I looked up and saw the aircraft directly above our aircraft at between 100-200 ft. vertical separation.I immediately called Dupage tower and asked them if they saw this other aircraft. They replied; 'no' and I said; 'ok; that was pretty close.' We continued on our way remaining in the pattern and landed shortly after.A corrective action for this would be a warning from the tower that another aircraft is departing the parallel and or a call to either aircraft letting them know they were on a collision course for each other.My aircraft could not see the traffic behind me and the other aircraft couldn't see ours because they were pitched up in a climb.