Cook also had a 66 to match Chapman at 7 under after a more forgiving day at Harbor Shores. Chapman had a 67.
Michael Allen set a course record with a 64, recovering nicely from a first-round 77.
Starting his round on the back nine, Irwin birdied four of his first six holes. He has won the major championship four times, although not since 2004. He was the 54-hole leader last year at Valhalla but finished fourth.
Chapman led by a stroke after the first round and didn't make a bogey Friday until the par-5 ninth, his final hole. Irwin also bogeyed No. 9.