Fox had eight birdies, including seven in his last 11 holes, in a flawless eight-under 64 at Mount Juliet on Thursday.
He has a one-shot lead over Frederic Lacroix, Jorge Campillo, Fabrizio Zanotti and Marcel Schneider.
Fox, who lost a playoff for the 2018 Irish Open to Scotland's Russell Knox, won the Ras Al Khaimah Classic in February, finished runner-up in the Soudal Open and Dutch Open and was third in the BMW International on Sunday.
"I'm more surprised, to be honest, than anything else," the 56th-ranked Fox, son of All Blacks World Cup winner Grant Fox, said.
"I've been fighting it on the range the last couple of days and a 64 certainly didn't look likely early in the round.
"I made a couple of birdies but I was scrapping away and hit a great wedge on my eighth hole (the 17th) and made a few putts as well.
"So just one of those days that shows how important patience is in a round of golf."
Three-time major winner Padraig Harrington shot a two-under 70 just days after his victory in the US Senior Open, while 2019 Open champion Shane Lowry had to settle for a 71.
"It's a pity with the finish," said Harrington, who bogeyed two of his last three holes. "It's just a part of the game, isn't it?"
Lucas Herbert was the best of the Australian contingent, shooting a three-under 69, while Maverick Antcliff went round in 71, one better than both Scott Hend and Min Woo Lee.