Annika Sorenstam, the four-time defending champion, also shot 67 to remain one shot back at minus-13.
Jenny Rosales, a two-time winner on the LPGA Tour, fired a 7-under 65 to move into third place at 12-under-par 132. Karrie Webb and Women's British Open champion Jeong Jang are one shot further back at minus-11.
The field this week is comprised of 43 LPGA Tour players and 35 players from the Japan LPGA circuit. The event is 54 holes and has no cut.
Kim opened with a birdie on the first. She drained a birdie putt on the par-3 fifth and made it two straight as she birdied the par-5 sixth to get to 12 under at Seta Golf Course.
The 25-year-old Korean parred her next two holes before catching fire around the turn. Kim poured in a birdie putt on No. 9. She came right back with a birdie on the 10th and made it three in a row as she birdied the 11th.
That birdie got her to 15 under and four strokes clear of Sorenstam. Kim then stumbled to back-to-back bogeys from the 12th to slide back to 13 under, but she still led to three.
Kim, who has 12 top-10s over the last three years, but no wins, got one of those strokes back with a birdie on the 15th. She tripped to a bogey on 16, but atoned for that error with a birdie on 17 to get back to minus-14. Kim parred the last to remain there.
Sorenstam, who is trying to become the first person in LPGA or PGA Tour history to win an event five straight times, also started her round with a birdie at the first.
The 34-year-old parred her next four holes before a birdie on the sixth got her to 10 under. Sorenstam made it two straight as she birdied the seventh. After four pars in a row, she tripped to her first bogey of the event at the par-3 12th.
Sorenstam, who won by nine strokes each of the last two years, stood at 10 under, four behind Kim, with six holes to play. The top player in the women's game turned it on down the stretch. She birdied the 14th for the second straight day.
After a pair of pars, Sorenstam birdied the 17th and 18th to get to 13 under within one stroke of Kim. The 67 was Sorenstam's 10 consecutive round in the 60s at this event.
Sophie Gustafson posted her second straight round of 5-under 67 on Saturday. She shares sixth place at 10-under-par 134 with Japanese LPGA Tour player Shiho Ohyama, who posted a 3-under 69 in the second round.
Karine Icher and Sakura Yokomine are tied for eighth place at 9-under-par 135. Reilley Rankin and Sherri Steinhauer lead a group one stroke further back at minus-8.