He posted an eight-under 208 total, with South African Branden Grace (70) and American John Huh (71) the closest challengers at seven-under heading into the final round.
Seven others are two shots back, including halfway pacesetters Tony Finau and Bud Cauley, who both shot 74.
Nobody carded better than 68 after a cold front blew through and brought with it winds gusting to 30 miles per hour (48 kph), sending the average score soaring to 74.3 strokes.
Chappell finished runner-up four times on the PGA Tour last year, and is still seeking his maiden victory in his 180th start.
He was in full survival mode early and was delighted with the way he hung tough.
“The golf course hit me in the chin real hard early,” he told PGATour.com. “I just couldn’t find a rhythm. To make the turn only two over after some of the places I hit it, I was confident if I could get to the 14 tee at two over par or better, that I could post a score.
“To birdie 14, 16 and 17 obviously felt sweet and a couple of good par saves on 15 and 18 I showed a little emotion and showed that it meant something to me.”
World number 21 Grace, a low-ball hitter, described the conditions as similar to the first two rounds at the Masters, where cold temperatures and strong winds also wreaked havoc.
“That was brutal,” he said. “It was really tough, just trying to stay alive, trying to make birdies, even the pars were tough.”
(Reporting by Andrew Both in Cary, North Carolina, editing by Gene Cherry)
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