Henley took double bogey on No. 7 and answered with a 30 on the back nine of the TPC Sawgrass for a 7-under 65. That gave him a two-shot lead among the early starters in warm, calm conditions that were perfect for scoring.
Lee Westwood, Jordan Spieth and Sergio Garcia were among those at 67.
Rory McIlroy was challenging for the lead until three bogeys dropped him to a 70. Phil Mickelson, off to the slowest start of his PGA Tour career, had to make a 6-foot par putt on his last hole for a 75.
Adam Scott was among the late starters.