Chapman had a 67 on a more forgiving day at Harbor Shores. Both leaders were at 7-under for the tournament.
Hale Irwin shot his age (66) but was so frustrated afterward he said he might switch putters before playing again.
"I know the greens are difficult, but some of the putts I missed today are not that difficult," said Irwin, who trails the leaders by two shots. "So I'm a little discouraged with that to the point where I might even change to another putter (Saturday) that's similar, but a different putter. I can't putt any worse."
Michael Allen broke the course record with a 64, recovering nicely from a first-round 77.
But Irwin was the focus afterward. He even arrived for his post-round news conference while Cook was still finishing his.
"When you can shoot your age in a major championship, they ought to give you bonus points," Cook said. "Lift, clean and throw or something -- for the rest of the week."
Chapman, from England, 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.
That was the lone blemish on Irwin's scorecard, but he was disappointed he didn't shoot an even better score.
Starting his round on the back nine, Irwin birdied four of his first six holes. He went on to add birdies on Nos. 2 and 5.
Most of Irwin's birdies came on short putts from about 5 feet and in. The par-5 fifth was the exception.
"A long putt there -- made one of about 12 feet," Irwin said. "Really a big putt, in case you can't see the cynicism in my comments."
Irwin has won this major championship four times, although not since 2004. He was the 54-hole leader last year at Valhalla but finished fourth.
He has won a record 45 times on the Champions Tour, but not since 2007.
Steve Pate (69) and Loren Roberts (67) were tied for fourth, two strokes behind Irwin. Joel Edwards (67) and David Frost (70) were another stroke back, and Allen was part of a larger group at 1 under.
Allen, the 2009 champion at the Senior PGA, is the Champions Tour's money leader this year. No player has recovered from a first-round 77 to win this event, but Allen is at least back in the picture after a terrific performance Friday. He hit 17 greens in regulation after reaching only seven in his first round.
"I didn't get too overly dramatic about it, but I knew I had to play a good round today and I didn't want to come out here and embarrass myself," Allen said. "I love the challenge, like on the tour, of playing a really hard course, and that's what this is."
After a windy opening day, scores dropped by an average of nearly three strokes at the 6,822-yard course next to Lake Michigan.
"A lot cooler," Chapman said. "It was very hot yesterday for us English boys. It was 88 or something I think yesterday."
There are still two days remaining, and conditions easily could take a turn for the worse. Earlier this week, players were apprehensive about the difficulty of the greens on the Jack Nicklaus-designed course.
Irwin likened it to the 1974 U.S. Open at Winged Foot, which he won at 7-over par.
"There was a lot of disgruntled players in '74, and 70 percent of them were out of the tournament before the tournament even started," Irwin said. "I think we saw some of that perhaps this week when you see these greens. And they can be maddening. There's no doubt about it."
Information from The Associated Press was used in this report.