GA flight instructor reported an NMAC while approaching the airport and took evasive action to avoid the other aircraft.

Narrative

We were maneuvering in the south practice area around Maricopa town (to avoid congestion in SE practice). After various maneuvers; we descended to 3500 and started heading to Gila River Memorial (abandoned airfield) to do Eighths on Pylons. Once we got closer; we descended to 2100 to conduct the maneuver. There were no traffic conflicts during the maneuver. Upon completion; we departed the area southwest bound to climb up a bit (about 3000 MSL) and to run the approach checklist. We then turned eastbound towards CHD. We were on with Chandler tower about to enter their airspace to do some pattern work. We initially contacted CHD tower on 133.1; then the tower advised us to contact the tower on 126.1 since we are coming from the west. This is where the conflict started to arise. There was traffic coming from the west (unknown callsign; was a twin-turboprop) that appeared to be heading towards Chandler as well (heading eastbound around 3000 ft MSL). At around XA:20 local time the aircraft then started heading towards the North to an unknown airport. The aircraft looked as if it was going to pass behind us (still 3000 MSL); but this aircraft was going much faster. We appeared to be on a converging course. At XA:21 I took over the flight controls and had to abruptly maneuver the aircraft (climbing left turn (to remain outside CHD Delta)) and we promptly got a visual on the converging aircraft. They ended up passing off our left side about 400 ft below us (they stayed at 3000 MSL and proceeded NNW bound). We then continued our left turn and went to CHD for pattern work. Upon entering CHD we were very stirred up due to this stressful event and mistaken CHD TPA for 1900 (this is TPA for rotorcraft). Tower then corrected us; and we promptly climbed to the correct TPA (2300).