Harrison Frazar posted a 65 to move into second place at minus-9. Camilo Villegas (65) and Ryan Moore (67) share third place at 8-under-par 202. Steve Flesch, Trevor Immelman and Peter Lonard are one stroke further back at minus-7.
Henry got off to a solid start with three pars over his opening four holes. At the third, he dropped in a birdie to move to 5 under. Henry kept climbing the leaderboard with birdies on five and seven.
The Connecticut native got within one of Stewart Cink's lead with a birdie on No. 9. Henry rolled in a birdie putt on the 11th to gain a share of first.
Henry knocked his third shot to two feet at the par-5 13th to set up his sixth birdie. He ran home a 14-footer for birdie at the 15th to grab a two-stroke cushion over Frazar, who was already finished.
The 31-year-old Henry converted a 24-footer for birdie on 17 at the TPC at River Highlands to move three clear.
However, he was unable to save par from a greenside bunker at the last to lead by two after three rounds. That was his first bogey since his 17th hole during Friday's second round.
'It was great. It was one of those days I thought I was capable of starting out the week,' Henry said. 'I made a couple long putts coming in so that made the day.'
Henry, who was born in Fairfield, won the 1994 and 1995 Connecticut amateur championships. He leads after 54 holes for the first time in his PGA TOUR career.
'Playing at home, so to speak, you sometimes put too much pressure on yourself,' Henry admitted. 'However, I got hot with the putter today, plus I kept the ball in the fairway and gave myself a lot of birdie chances. Obviously, I am in a great position and today was really special with everyone rooting me on.'
Frazar was meandering through his front nine with three bogeys and two birdies that left him 3 under at the turn. The back nine was a totally different story though.
'I had a ho-hum start,' Frazar admitted. 'I didn't feel that great. I hit a couple of bad shots that ended up in some bad places and had to make some bogeys.'
The 34-year-old birdied the par-4 10th to get back to even-par for his round. Frazar made it two straight as his birdie effort from just inside 13 feet on the par-3 11th found the bottom of the cup.
Frazar kept rolling with a birdie, from 13 feet out, on 12 that got him to 6 under. He wasn't done either, as he sank his fourth birdie in a row on the par-5 13th after pitching his third to 11 feet.
The Texan then birdied 14 (21 feet) and 15 (eight feet) to make it six straight and get within one of Henry's lead. Frazar could only par the final three holes to end two back.
'I felt great with the putter,' Frazar said. 'You never expect yourself to make that many 15- and 20-footers, but you've got to have a few lucky breaks to go along with it. You never expect to make six birdies in a row.'
Mathias Gronberg posted a 5-under 65 to move into a share of eighth place at 6-under-par 204. He was joined there by Todd Fischer, Hunter Mahan and Joe Ogilvie.
Cink, who led by two after birdies on the first three holes, tumbled into a share of 21st at 4-under-par 206 as he played his final 15 holes in 5 over par.
He was joined at minus-four by second-round leader Darron Stiles, who struggled to a 4-over 74 with 14 pars and four bogeys on Saturday.