Jill McGill and Women's British Open champion Karen Stupples are tied for third place after posting rounds of 5-under-par 67.
LPGA Tour Rookie of the Year, and this week's defending champion, Shi Hyun Ahn was one stroke further back at minus-4. She was joined there by Ju-Mi Kim, Young-A Yang and two-time winner this year, Lorena Ochoa.
Women's world No. 1 Annika Sorenstam posted four birdies to go along with three bogeys in a round of 1-under-par 71, which put her in a tie for 18th.
Park, playing in the final group with Sorenstam and Ahn, opened with a birdie at the par-4 first. She picked up her second birdie at the par-3 seventh at Nine Bridges Golf Club.
The Seoul, South Korea native birdied the ninth from 6 feet out and made two in a row with a birdie on No. 10. Park moved to 5 under as she birdied the par-5 12th. However, she tripped to a bogey at the next after missing the green.
Park atoned for the error with a birdie on the 16th. She closed with a two-putt birdie at the par-5 closing hole to grab a piece of the lead.
'I am happy to finish 6 under. I kind of have some regret, but I am satisfied with the way I played today,' said Park, who won her first major earlier this year at the Kraft Nabisco Championship. 'I pushed most of my shots today, so my ball went to the right today. I made a couple of mistakes with some iron shots, and I kind of regret those shots.'
Koch was on fire early in her round. She started on the 10th tee and picked up a birdie there. She came right back with a birdie at 11. Koch birdied the 12th from 15 feet out to keep her roll going.
The three-time Solheim Cup performer completed a run of four straight birdies at the 13th by sinking another 15-foot birdie putt. Koch parred her next four holes, before a birdie on No. 18 helped her to make the turn in 5-under 31.
Koch moved out in front at 6 under as she picked up a birdie at the par-4 fifth. However, she stumbled to a three-putt bogey at the next. The 34-year-old came back with a 15-foot birdie putt at the eighth, her 17th, to get back to minus-6. Koch parred the last to share the first round lead.
'It was a great day of golf for me,' said Koch, whose only win came at the 2001 LPGA Corning Classic. 'I had a very nice start with four birdies on the first four holes. I did not quite continue that, but I played pretty good golf and made some pretty good putts. I hit my driver well today and kept it in play.'
Stacy Prammanasudh and a pair of Koreans, Mi Hyun Kim and Young Kim, are tied for ninth place at 3-under-par 69. Dorothy Delasin, Jeong Jang, Seol An Jeon, Catriona Matthew, Hyun Ju Shin and Angela Stanford were one stroke further back at minus-2.