One shot behind Thompson are Sandra Gal of Germany and Kris Tamulis at the Pete Dye-designed course located inside the famous 2.5-mile racing oval.
Two shots out of the lead are Moriya Jutanugarn of Thailand and Lydia Ko of New Zealand.
Thompson was sharp. She used only 26 putts and hit every fairway but one and 16 of 18 greens in regulation. The 63 was her second-best round of the year, falling short of a 61 she posted at the Pure Silk-Bahamas LPGA Classic.
"It was just overall a very solid round," Thompson said. "It was quite the early morning, so it was a bit cold on the range and struggled a bit on the range, but I just hit a few good drivers at the end and I just committed to one thing going into the round and I think that's what made my day a lot easier on me.
"I just stuck to my routine and committed to my golf shots.
"That round definitely gave me the confidence that I can make those birdies if I just let it go and fire at pins and just commit to my shots and don't doubt it."
Tamulis and Gal had bogey-free rounds. Last week, the 36-year-old Tamulis posted her best finish of the season with a tie for 15th at the Cambia Portland Classic.
"I putted good and been hitting it a lot better, which thank goodness because I've been really hitting it all over the park," Tamulis said. "So I didn't necessarily think that I was going to shoot 8 under."
Gal birdied four of the first five holes and three of the last four. The 32-year-old has only four top-20 finishes this year.
"I struck it pretty well out there and then I made a few good putts," Gal said. "I've been feeling like my game's been pretty good the last couple months, but I just haven't been scoring, so everything just came together."
Jutanugarn and Ko also played bogey free. Ko's 65 is her lowest opening-round score of the year.
"Obviously with our last major next week, you want to go in with good momentum and good results where it gives you confidence," Ko said. "All I can do is just try my best to have a lot of fun."
Amy Olson is three strokes behind Thompson at 66 along with Candie Kung of Taiwan and Nanna Koertz Madsen of Denmark.
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