Chappell, who started his round at the 10th hole, made nine birdies in a bogey-free round, catching fire from the 16th, his seventh hole of the day.
The little-known, 27-year-old American made eight birdies in an 11-hole stretch from there, including four in a row from the third hole and just missed a final birdie opportunity at his last hole to finish the day with an 11-under-par 202 total.
"Here, in the wind...if you would have told me someone was going to shoot 62 today, I would probably have laughed at you," Chappell told reporters after his spectacular round.
"I had a chip-in and then I just really holed all the putts that you kind of expect to hole that you don't always hole - a lot of 10- and 12-footers to make birdies. Just was able to keep doing it."
The Californian, who began the round at two under par, surged up the leaderboard and briefly held a share of first place with compatriot Gary Woodland while the round was ongoing.
"Once you get things moving positively, it becomes easy for that mind-set to change and to start swinging a little more confidently and hitting some more confident putts," he said.
Chappell, a 2010 winner on the Web.com tour, has yet to break through with a victory on the PGA Tour but this season has registered three top 10s including a runner-up finish at the Memorial to Matt Kuchar.
After nearly losing his tour card last season, Chappell, who played his college golf at UCLA, vowed to change his ways this season after a chaotic 2012.
"I went through two swing coaches, four caddies, and just never really had any structure, and that was kind of the goal for the year, to have some structure," said Chappell, who uses Mark Blackburn as his swing coach and James Sieckmann as a putting guru.
The intense Chappell, who has a wedding date set next month with fiance Elizabeth Petrie, believes it is all coming together.
"I feel like I'm in a good spot," he said.
"For me, perspective is a big thing. Went to the 9/11 Memorial on Wednesday with Elizabeth, and you know, it just really puts golf in its place.
"It seems to be whenever I get too caught up or too emotional about my game, life hits me hard. That was a great experience and a learning one for me, and it really kind of tightened my screws mentally."
The last time The Barclays was held at Liberty National, in 2009, unheralded Heath Slocum claimed the title. Slocum was also coached by Blackburn.
"Believe me, I've heard the history of this event and Heath and look forward to keeping Mark's batting average as high as we can," said Chappell.