Jiyai Shin, the LPGA Tour's leading money winner this season, shared second place at 67 with Paula Creamer and Mariajo Uribe. Catriona Matthew and Eun-Hee Ji both had a 68 at the Guadalajara Country Club to tie for fifth place.
Tournament host Ochoa shot a 71 and was tied for 13th.
Kim was already 2-under for her round when she began her birdie streak at the seventh. She closed with another birdie at the par-5 18th.
"I was very relaxed because I just came from Korea," Kim said. "I am still very tired from the time change, so I'm trying to not play too hard. I just want to play easy."
Michelle Wie was among those who shot a 69 Thursday.
Defending champion Angela Stanford had a 73.
Copyright 2009 by United Press International.