Only 12 of the 81 players in the event failed to break par on a Rock Barn Golf & Spa course that is known for yielding low scores. Tway shot a 62 on this course last year on his way to a fourth-place finish.
Tway, who had eight wins on the regular tour, including the 1986 PGA Championship, is looking for his first victory on the Champions circuit.
He had a one-shot lead over Tommy Armour III, Joe Ozaki, Mike Goodes and Mark Wiebe. Mark Calcavecchia, Mark O'Meara and David Eger were all two shots back in a tie for sixth.
Tway played the first 13 holes in 9-under par, giving him a shot at what would have been the first sub-60 round in the history of the Champions Tour. Those thoughts quickly ended, however, when he bogeyed the par-5 14th.
"I had a good round here on the last day last year, but the conditions were different," Tway said. "We all knew scores would be low this week. I putted very well, but did not play flawlessly."