Hale Irwin, meanwhile, shot his age to give himself a chance to become the oldest winner in the history of the Champions Tour.
The Golf Club at Harbor Shores on Lake Michigan was set up to make lower scores possible Friday and the winds calmed to a large degree.
Cook shot a 5-under 66 and Chapman, the first-round leader, had a 67. That left them tied at 7-under 135 after 36 holes over the Jack Nicklaus-designed course.
Irwin, nearing his 67th birthday and a record four-time winner of this major championship, was just two shots behind after firing a 66.
Michael Allen shot the low round of the tournament, a 64, to finish in a tie for eighth at 141.
The spotlight on the weekend could fall on Irwin, who has a chance to add to his historic golfing totals.
A victory this week would allow Irwin to break the record held by Mike Fetchick as the oldest winner on the Champions Tour. Fetchick won the 1985 Hilton Head Seniors International on his 63rd birthday.
Irwin has 45 Champions Tour titles, but none since 2007. He has finished among the Top 10 on the senior circuit a staggering 206 times. He won the first of his three U.S. Open titles on the regular tour 38 years ago.
Swim Week Miami Beach 2014 [PHOTOS]