Defending champion and third-ranked Justin Thomas, who won CJ Cup two of the last three years in South Korea, had a tap-in birdie on the last hole for a 68 and is five shots back in a tie for sixth with Jason Day of Australia, who holed out from 23 feet on the 11th hole to highlight at 66, and 10th-ranked Tyrrell Hatton of England, who didn't make a birdie until the last hole with struggling to a 73.
McIlroy is still to register a worldwide victory in 2020, with the world number four looking for a strong finish to the week to put pressure on those at the top of the leaderboard and make a late challenge for a 19th PGA Tour title.
Henley birdied three holes in a row on Nos.
As reported by Sky Sports, McIlroy said after his performance: 'I think after the three weeks off after the US Open and getting home and recharging, I sort of viewed this as like a six-week run-up until Augusta, ' McIlroy said. "Some of those holes you're not really trying to birdie them, you're kind of just trying to leave yourself an uphill 35-footer and fortunately I made a couple of them", he said. "Gives me confidence to know it's working so well".
"It was kind of a tie". That was a big plus. "I've got to just keep my head down and play a good round for me". But the irons feel good and the putter feels great.
When asked whether he can the trophy he added: 'There's not much separation, so I would need to go out and maybe shoot 64 tomorrow and see where that leaves me.
"I'm just trying to play my game and stay confident. I did what I wanted to do and that's all I can ask for".
The Colombian Sebastián Muñoz emerged as the best golferLatin American by completing the day with an excellent record of 67 strokes (-5) which allowed him to climb 10 places in the general classification and place himself in tenth place with the sum of 208 hits (-8).
Four-time PGA Tour victor Xander Schauffele, who led the pack headed into the weekend, slipped down the leaderboard after carding a disappointing two-over-par 74 to share second place with fellow Americans Talor Gooch (69), Jason Kokrak (68) and Lanto Griffin (66).
Henley was an unspectacular model of consistency in building his lead as he hit five birdies and had a bogey-free round.
Heading into the weekend four strokes back, Henley followed a 10-foot par-save at the third by holing from a similar distance to birdie the next, before getting up and down from a greenside bunker to birdie the par-five seventh.
Winter Drought Relief Unlikely in Western US
Wetter-than-average conditions are most likely from the Pacific Northwest, Northern Plains, Great Lakes and into the Ohio Valley. The greatest chances for warmer-than-normal conditions extend from the Southwest, across the Gulf states, and the Southeast.