She finished the two rounds of stroke play at 10-under-par 134, which was two better than Ha Na Jang, who shot a 5-under 67 on Tuesday.
Mina Harigae, who won this year's U.S. Women's Amateur PubLinks, posted a 3-under 69 and is third at minus-7. Kristen Park carded a 2-under 70 and is fourth at 6-under-par 138.
Kim, the reigning U.S. Women's Amateur champion, began on the 10th tee and birdied her first hole. She birdied the par-4 12th, but went on a run of poor golf.
She bogeyed 13 and 14, then double-bogeyed the par-3 15th. Kim atoned for the error with a birdie at 16 to make the turn at 1 over par.
Kim played better on her second nine with a pair of pars in her first two holes. She then traded birdies and bogeys the rest of the way to shoot a 34, but still get medalist honors.
Alexis Thompson, who at the age of 12 was the youngest player to ever compete in the U.S. Women's Open, shot a 4-under 68 on Tuesday. She is tied for fifth place with Evan Jensen (72), Sally Watson (71) and Jennifer Johnson (71) at minus-4.
Tzu-Chi Lin (69), Michelle Shin (71) and Sue Kim (69) shared ninth place at 3-under-par 141.
Jenny Shin will not be successfully defending her title. She missed the match-play cut, which was 7-over-par 151, by two strokes.