After opening with a 72, she had a 64 the best round of the week in the 36-player event Friday to pull within a stroke of second-round leaders Anna Nordqvist, So Yeon Ryu and Pornanong Phatlum.
Kim, who won the event in 2010, birdied the final two holes for a 67 and had only 22 putts in the round.
"I really like this golf course," Kim said. "I have a good feeling for the course, and I've been practicing. It's just nice to see the result."
Third-ranked Stacy Lewis was third at 11 under after a 67.
Ryu was another stroke back after a 71. Nordqvist and Pornanong each shot 72 to remain 9 under.
Top-ranked Inbee Park, No. 2 Suzann Pettersen and Lizette Salas were 8 under. Pettersen had a 70, Salas shot 71, and Park 72. Michelle Wie, the 2009 winner, was 7 under after a 67.
Tournament host Lorena Ochoa won 27 LPGA Tour titles before retiring in 2010
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