Chappell trailed by as many as four shots on the front nine. He took the lead on the 17th hole with a 10-foot birdie as Johnson went from rough to rough to sand to a double bogey. Chappell shot a 68.
They were at 8-under 202, just two shots ahead of Rory McIlroy and Ryan Moore, who each shot 66.
Johnson can win the $10 million FedEx Cup bonus with a victory or by finishing second alone. McIlroy has to win and needs Johnson to finish in a two-way tie for second or worse.