He saved par from six feet at the final hole to post a seven-under 133 halfway total, while Chappell (68) missed a good birdie chance at the last to end the day on six-under.
Johnson and Chappell separated themselves from the pack, with third-placed Kevin Kisner and Japan's Hideki Matsuyama four strokes from the lead at three-under 137.
If Johnson wins on Sunday, he will also claim the FedExCup and the $10 million (8 million pound) prize awarded to the winner of the season-long points race.
"I felt I played really, really solid today. I just didn’t really get a lot out of it," Johnson told Golf Channel after a round that included five birdies and two bogeys on a course with punishing, wiry rough.
"I just didn’t really get a lot out of (the round), some close looks I didn’t make and I missed a short par putt on 17 and not birdying the last hole on 18, I felt I left a few shots out there.
"Three-under’s a great score around here, I’m never going to be upset with that but I felt I played really well today."
The long-hitting world number two has elevated his game in recent months, winning his first major at the U.S. Open, followed by a World Golf Championships victory and a triumph at the BMW Championship in his last start.
He has harnessed his prodigious power with a stellar short game for what has often proved unbeatable.
"I’ve got a lot of control with my ball," he said. "This course is difficult. You’ve got to drive it straight, control your irons coming into the greens.
"I’m really comfortable with the swing. I’m swinging really well. The biggest key is just putting in the work."
The Tour Championship is the only event on the PGA Tour that hands out two trophies, one to the tournament winner and the other to the FedExCup champion.
Johnson started the week as top seed for the FedExCup and one of his chief rivals disappeared on Friday when Australian world number one Jason Day pulled out with a continuing back problem.
(Reporting by Andrew Both in Cary, North Carolina; Editing by Larry Fine)
