Bradley had five birdies along with his eagle in a bogey-free, 7-under-par 65. He is two strokes ahead of Swedes Fredrik Jacobson and Alexander Noren and fellow American Bo Van Pelt.
Bradley, who won the Byron Nelson Championship and the PGA Championship earlier this year, started on the second nine Thursday and opened with a birdie at the 10th hole. He added another at 14 before posting a 3 at the par-5, 538-yard 18th hole by dropping a 15-foot putt.
He also had birdies at Nos. 2, 5 and 8 for his 65.
Jacobson was 4-under over his final three holes, carding an eagle 2 at the 16th hole and birdies at 17 and 18. He had three other birdies and a pair of bogeys. Noren started his round with a bogey but had six birdies and 11 pars the rest of the way. Van Pelt twice had three-birdie strings in his round.