Kim birdied five of the final six holes as darkness fell for a five-under 65 and the second-round lead. The 27-year-old South Korean closed with a six-under 29 on the front nine, tying Karrie Webb (2001) and Sarah Kemp (2011) for the lowest nine-hole score in the event.
A 10-time LPGA Tour winner, Kim is looking for her first major victory. She was runner-up at the 2015 PGA Championship and tied for second at the Evian Championship in 2018.
The last four winners of the tournament either led or co-led after 36 holes.
Jennifer Kupcho (65), Danielle Kang (69), Carlota Ciganda (69) and Anna Nordqvist (68) were a stroke back.
Meanwhile, Ryan Fox is also in title contention on the men's European Tour after posting a two-under 70 in his second round.
Fox couldn't quite match his opening-round fireworks, where he shot a four-under 68 at the Wentworth Golf Club, but still did enough to stay within touching distance of leaders Shane Lowry and Matthew Fitzpatrick at 12-under.
The one-time European Tour winner now sits at six-under for the tournament in a tie for 10th place.
Danny Lee posted an even-par 71 in the second round of the Shriners Hospitals for Children Open on the PGA Tour to miss the cut by five shots.