If he does, he'll join Arnold Palmer and Bernhard Langer as the only back-to-back winners of this PGA Tour Champions major.
McCarron and Bart Bryant shot matching 65s on Saturday to move into a share of the lead with Jeff Maggert.
McCarron birdied two of the final four holes at Exmoor Country Club for a three-round total of 16-under 200. Last year, he rallied to win the event at Caves Valley near Baltimore.
Maggert, who led most of the day, shot 66.
Vijay Singh (66) was one shot back. Three-time champion Langer (67) and Illinois golf coach Mike Small (66) were another stroke behind, and Scott Parel (70) was in a group at 13 under.
McCarron came into the week with seven top-10 finishes this year and a win at the American Family Insurance Championship last month.
"The only way to repeat is you've got to put yourself in position going into the final round, which I've done," he said. "(Sunday) will be very exciting. We've got a stacked leaderboard, and someone is going to have to go pretty low tomorrow to win this tournament."
It's the first time three players have been tied for the lead entering the final round of a major since the 2011 U.S. Senior Open, when eventual winner Russ Cochran was even with Mark Calcavecchia and David Frost.
McCarron opened with a birdie on the par-5 first hole and finished with eight birdies and one bogey on a rainy afternoon. He came on strong on the back nine, making three straight birdies starting with the par-4 10th. He added two more on the par-5 15th and par-4 17th while also limiting his mistakes.
"I hit the ball very well," he said. "I hit a lot of fairways, hit a lot of greens. I went after the hole locations that were on the right side for me where I can hit my cut, and the hole locations on the left side I played a little safe. I did a very good job of managing my game today."
Maggert — who won both the Regions Tradition and the U.S. Senior Open in 2015 — came in anticipating a "birdie-fest" because of the soggy conditions and got off to a blistering start.
He opened with an eagle after his approach rolled to about 3 feet. With birdies on the par-4 second and fourth holes, he looked like he might build a big lead.
But he made just three birdies the rest of the way before a bogey at 16 dropped him into a tie for the lead.
"I felt like I needed to make six, seven or eight birdies today to keep pace with the leaderboard," Maggert said. "It kind of turned out that way. Not only was I making a lot of birdies, there was 10 or 12 other guys making birdies, too. We've got a jumbled-up leaderboard. I think tomorrow's conditions are going to be very similar to today, so I'm going to have to keep the gas on and make birdies."
Bryant played bogey-free and made four of his seven birdies in a five-hole stretch, starting with the par-4 seventh. Winning a major would be quite an accomplishment, given his difficulties in recent years on the course and away from it.
His wife Cathy died of brain cancer in April 2017, and he placed outside the top 10 in all 14 starts that season. This year, he has one top-10 finish in 10 events.
That much is likely to change, barring a collapse on Sunday. Bryant credits changing putters from a Bobby Grace to an Odyssey 2-Ball for helping his confidence.
He made the switch before the final round of the American Family Insurance Championship. Bryant bought the Odyssey at a Dick's Sporting Goods and then shot 66 the next day.
"I really haven't made a ton of putts out there," Bryant said. "I haven't made the long ones, but I haven't missed the ones I'm supposed to make, and that's been the big difference."
Lone Oak alum Kenny Perry shot a third round 69 Saturday and sits tied for 10th at 12 under.
