The Australian followed her opening-round 66 at Colombia Edgewater Country Club with a 69 on Saturday (AEST) to be nine-under for the tournament.
Kim is three shots adrift of Thai leader Arpichaya Yubol (66) and two behind Pajaree Anannarukarn (66), Sophia Schubert (66) and Hye-Jin Choi (67).
After beginning with three birdies in her opening seven holes to continue her fine form from the previous round, Kim dropped a shot at the par-three eighth - a hole she birdied on Friday (AEST).
The 25-year-old then made bogey on the par-five 10th, another hole she birdied in the first round.
A birdie on the very next hole, however, steadied her, and Kim made one more on the 13th without any further blemishes to finish tied fifth.
The 2025 Evian Championship winner sits in an elite group comprising major winners Haeran Ryu, who won this this year's KPMG Women's PGA and Evian Championship, and world No.2 Jeeno Thitikul.
Ryu shot 68 and Thitikul 67, with all poised to challenge Yubol at the weekend.
Robyn Choi, who opened with a 67, made 70 and is tied 17th at seven under. The Australian had three birdies with her only bogey on the first - her 10th.
"It's pretty good day for my putter," said the 24-year-old Yubol, who remains winless in four seasons on the LPGA Tour while also finishing second this year at Mayakoba and the ShopRite LPGA.
After making birdie on the par-4 17th to get to 13 under, Yubol bogeyed the last for her first bogey of the week.
"It's golf, so it always happens," Yubol said. "For me, 36 holes with just one bogey is amazing."
American Schubert was happy with her work on the greens.
"I had five or six weeks off at home leading up to this, and I worked really hard," Schubert said. "Worked on my putting because that's what I need to work on. It's just really been clicking, making putts."
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