Kerr went into the tournament ranked third in the world after having been briefly No. 1 this year. Current No. 1 Jiyai Shin is not playing this week while No. 2 Yani Tseng shot a 76 to open the tournament.
Na Yeon Choi, ranked fourth in the world, had a 68 and shared third place with Katherine Hull, Paula Creamer and Ai Miyazato.
Miyazato was also No. 1 in the rankings for a time this season, but has slipped to sixth place.
Defending champion Michelle Wie shot a 78 Thursday and then withdrew with a back injury.
"I was very excited to be here, but unfortunately I can't play anymore," Wie said. "We took an MRI and I have two little cysts near my spine and a little disc bulge. It's nothing major, but it's just something I can't play with right now."
Ochoa, the tournament host who is playing for the first time since announcing her retirement in May, shot a 74.
"It's good to be back," Ochoa said. "It would be better if I had a better round today."
Kerr's round was highlighted by a stretch of six birdies in a seven-hole stretch beginning at the ninth.