The Australian left-hander picked up three shots in his first nine holes after teeing off at the par-three 10th, then bogeyed the second before ending his round in style with birdies at the seventh, eighth and ninth.
That left Chalmers a stroke in front of long-hitting American Ricky Barnes and Swede Fredrik Jacobson, who carded matching 67s.
“I really drove the ball well, probably the best I have driven it all year,” Chalmers told PGA Tour Radio. “That kind of set up the rest of the round, and finishing with three straight birdies is always nice.”
Chalmers, who has twice finished second on the PGA Tour during his career, felt he was very fortunate to escape with pars on the only two occasions when he missed the fairway by more than a couple of feet off the tee, at the third and fourth.
“It’s nasty,” he said of the lush rough at Congressional. “I drove it in the rough twice, on my 12 and 13th holes, and I had real trouble. I had to lay it up and luckily I got them up and down (for par).
“You just have to be coming out of the fairway here (with second shots), and I did do that the majority of the time today.”
Defending champion Bill Haas launched his title defence with a 68, ending the day level with fellow Americans Patrick Reed and Erik Compton, and South African Tyrone Van Aswegen.
Eight players, including twice former U.S. Open champion Retief Goosen of South Africa and South Korean K.J. Choi, were knotted on 69.
Woods, playing in a high-profile grouping with compatriot Jordan Spieth and Australian Jason Day, initially looked rusty and struggled with seven bogeys in his first 12 holes before recording three birdies in his last six to shoot a 74.
“I made so many little mistakes,” Woods, who had surgery to repair a pinched nerve in his back in March, told reporters after finishing the round tied for 83rd in a field of 120. “But I played a lot better than the score indicated, which is good.
“The hard part was just getting into the rhythm of playing competitively. You play with your buddies all day for cash and stuff but it’s just not the same. It’s not the same as tournament golf, different level.”
Woods’ playing partners also failed to break par in the tough scoring conditions, Spieth carding a 74 and Day signing for a 73.
“It was a great group,” said Woods, whose opening 74 was also matched by U.S. Open champion Justin Rose of England and reigning PGA Championship winner Jason Dufner.
“Unfortunately, we didn’t see a lot of each other on the front nine. We were all kind of looking to break 80. It was a bit of a fight for all of us but we hung in there.”
(Reporting by Mark Lamport-Stokes in Los Angeles; Editing by Frank Pingue)