Rookie Chun, who earned LPGA Tour membership by winning the U.S. Women's Open in 2015, hit every fairway and green on the way to her lowest round since May's Kingsmill Championship.
The leading candidate for Rookie of the Year honours, world number seven Chun has posted nine top-10s this season, six of which were top-3 finishes.
"Before the round, I felt really nervous today, and it was windy, and there was a thunderstorm this morning, so I tried (to) more focus on my game," Chun said.
"I could see the putting lines very well, and I was so good rolling the ball on those lines."
Korean Park, a non-member of the LPGA Tour who led during this year's U.S. Women's Open where she tied for third, grabbed a share of the lead by sinking an 18-foot birdie putt at the 18th.
She has finished outside the top-13 just once in her six appearances on Tour.
Annie Park, another rookie contender, stayed close to Chun on Thursday as she posted a bogey-free 64, having switched to different irons just five days before the tournament.
"I didn't know my yardages coming in so I had to figure that out in the practise rounds," the American said.
World number one Lydia Ko of New Zealand, the Olympic silver medallist, opened with a 70 to trail the leaders by seven.
"It was tricky for me because on the back nine I really wasn't hitting fairways," said the 19-year-old. "I was making up and downs. It was a good thing my wedge shots or chip shots were good enough where I was able to get off with par."
"Hopefully I'll be able to hit some more fairways tomorrow."
Canadian Brooke Henderson, ranked third in the world, was one better than Ko with a two-under 69, while number two Ariya Jutanugarn of Thailand triple-bogeyed the 18th for 73.
(Reporting by Larry Fine in New York; Editing by Mark Lamport-Stokes)
