The 27-year-old Spaniard, a winner at the Spanish Open a fortnight ago, drained 10 birdies in a spectacular round on Friday to finish on 11-under-par 131 at Congaree Golf Club in Ridgeland, South Carolina.
Rahm's only disappointment came at the last when he closed with a bogey that cost him the outright lead.
As it stands, he shares the lead with American Kurt Kitayama, who added a second-round 65 to his opening 64 to join the Spaniard on 11 under.
"Right from the get-go my speed was good and felt confident and the rest of the game accompanied the putting," Rahm said.
"I hadn't putted on greens this fast in a while. Took me a little bit to get used to it. It's one thing to do it on the putting green. It's another to do it on the course."
Rahm's putter is red-hot at the moment. On Friday, he needed just 22 strokes on the green across 18 holes and sunk 125 feet of putts.
"I'm glad to have such a good putting day," he added. "I'm hoping to keep the pace as good as it has been the last few holes on the course and hopefully tidy up a few ball-striking mistakes."
Australia's Cam Davis and American Aaron Waise share third place a shot back, while world number two Rory McIlroy is lurking just one further stroke behind, two behind Rahm.
McIlroy mixed six birdies with two bogeys in a second-round 67 that leaves him well-placed for the weekend, although he knows it won't be easy trying to catch an in-form Rahm.
"Didn't feel like I was much off," he said. "On the back nine I just started to hit a lot more quality golf shots.
"It's tricky and the greens are super quick. If you're just a little off, they can punish you. Really impressive round of golf."