Chun followed her opening 64 with a three-under 69 on the Congressional Country Club course on Friday to get to 11 under as she seeks a third major championship title.
Heading the chase are world No.4 Lydia Ko (67) and in-form American Jennifer Kupcho (68).
Green, the 2019 champion, improved with a 69 to be among five players tied fourth, but seven shots behind Chun, as she pursues a second major crown.
"I would like to see this course a little bit firmer," Green said.
"I feel like with wedges today we were worrying about how much they were going to spin back, so if we can see them bounce and release a little bit more, I think that would suit me.
"It feels like kind of what we played in the practice rounds, so it actually has dried up significantly quickly. Hopefully it just gets firmer."
World No.3 Lee, the recent US Women's Open winner, is a further shot back at three under after climbing with a 68.
"Chasing is always fun," said Lee, who equalled the major championship record in coming from seven shots back to win her maiden major at the Evian Championship.
"You can try to be a bit more aggressive when you play."
Chun had led by five shots after the first round, equaling the biggest 18-hole advantage in the history of women's major championships
She looked like building a huge lead when she opened her second round with three birdies in her first five holes before bogeys at Nos. 7 and 8 took away some of her momentum.
Like Chun, Ko is trying for her third major title and first since 2016.
Kupcho took the first major of the season in early April in the California desert and won a playoff Sunday in Michigan for her second LPGA Tour title.
LPGA rookie Steph Kyriacou is tied 27th on even par after a second straight 72 while fellow Australian Srah Kemp shot 74 is three over.
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