Chappell, looking for his first PGA Tour win, was 12 under par for the opening event of the FedExCup playoffs with playing partner Woods one off the pace after making three birdies in four holes from the fifth.
Nine players were within three shots of the lead including clubhouse leader Graham DeLaet of Canada, who fired a 65 for a 10-under-par total of 274, one shot better than Phil Mickelson who also posted 65.
Tied with Woods on 11-under were overnight co-leaders Matt Kuchar and Gary Woodland.
On the course at 10 under par were Masters champion Adam Scott of Australia (through 14), U.S. Open winner Justin Rose of England (12 holes) and former Masters champion Bubba Watson (10).
Chappell, who set a course record with a nine-under-par 62 on Saturday, was playing with steely steadiness, parring his first seven holes before making birdie at the eighth to reach the turn one-under for the day.
Kuchar and Woodland both bogeyed the first hole, with Kuchar running off a series of pars and Woodland balancing two birdies with a double-bogey at the fifth after an errant drive.
British Open champion Mickelson began the day tied for 34th, nine shots back, but rocketed up the leaderboard and got to 10-under before giving a stroke back with bogey at the last.
"I love playing here," said Mickelson at home on the course as a Barclays spokesman and a member of Liberty National.
"The people are really fun to play in front of," said Mickelson, a fan favorite who finds the banter with spectators entertaining.
The back nine at Liberty National also promised some competitive fun on a sunny day on the edge of New York harbor.