Two-time major winners Collin Morikawa and Justin Thomas are also three shots adrift of Henley, along with Patrick Cantlay.
World number two Rory McIlroy was three under at the turn but lost momentum on the back nine.
The Northern Irishman made bogeys on the 14th and 17th to cancel out birdies on the 11th and 15th but allowed himself a smile after making a fortuitous birdie on the 18th.
The Masters champion completely misjudged a wedge out of the greenside bunker on the par-five, but his ball cannoned the stand at the back of the green and bounced back on to the putting surface. It left McIlroy a putt of 17 feet for a four and a round of 66 to leave him in a tie for eighth.
Englishman Justin Rose recovered from a error-strewn start to finish at one under having been three over at the start of the back nine.
Some 22 of the 30-man field walked back into the clubhouse under par. Six were on level par, and just two players, American Maverick McNealy and Austria’s Sepp Straka, were over par.
With the course having been subjected to heavy rain over recent days, the first round was played under preferred lies rules, allowing golfers to lift, clean and place balls in preferred spots if they landed on the fairway or other closely mown areas.
With more inclement weather forecast for Friday, second-round tee times have been moved to begin from 08:00 local time (13:00 BST).