The 29-year-old Californian also recorded four birdies and a lone bogey to post an 11-under total of 131, to stand one ahead of Swede Freddie Jacobson and American Kevin Kisner.
Jacobson carded a five-under 67 on the Plantation Course while Kisner, the overnight leader who is also bidding for a first victory on the PGA Tour, returned a three-under 67 on the Seaside layout.
American Kyle Stanley was alone in fourth at nine under after shooting a four-birdie 67 on the Seaside Course.
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Chappell, who has twice been a runner-up on the PGA Tour, was elated with his eagle at the 15th after not benefiting from what he had viewed as a well-struck approach from the right rough.
"I thought I hit a pretty good second shot there," Chappell told Golf Channel. "The wind obviously knocked it down and I just told myself, 'Hit the bunker shot harder than you want to.'
"Obviously I hit it hard enough," he said with a grin about his hole-out from 45 yards. "The wind blew a lot harder today and we are very fortunate the course is in great shape.
"It's soft so it makes some of the fairways play wider than they are, so you can get away with some missed shots as long as you are playing the wind properly."
British Open champion Zach Johnson, the American world number 10 who is the highest-ranked player in the field, posted a second successive 70 to end the day right on the cut line, a distant nine strokes off the pace.
Also advancing to the weekend after carding consecutive 70s was tournament host and next year’s United States Ryder Cup captain Davis Love III.
(Reporting by Mark Lamport-Stokes in Los Angeles; Editing by Larry Fine)
