Annika Sorenstam, Laura Diaz, Grace Park, Karine Icher, Gloria Park, Vicki Goetze-Ackerman and Emilee Klein were all tied for fourth at four-under-par 68.
Kim, the 1999 Rookie of the Year on the LPGA Tour, got off to a fast start at the picturesque Evian Masters Golf Club with two birdies over the first three holes.
At the par-4 fifth, Kim landed a 9-iron one foot from the cup. She tapped in for birdie and knocked a 6-iron within four feet at the very next hole to reach 4-under.
Kim then went on a stretch of nine straight pars while other players in the field attempted to secure the top spot.
McKay opened with three birdies over the first four holes before running into trouble with a bogey at the fifth. She added birdies at the seventh and the ninth but made back-to-back bogeys from the 10th to fall to two-under.
McKay recovered with a 15-foot birdie at the 14th and closed with back-to-back birdies from the 17th to enter the clubhouse at five-under-par 67.
'I hit the ball really well, I just made two mistakes on the greens that cost me two bogeys, and I had one bad drive that cost me a bogey,' said McKay. 'But overall, I struck the ball really well, and I putted well. So I am very pleased.'
Koch drained a 10-foot putt for eagle at the par-5 seventh before going on a run of three consecutive birdies from the eighth to move to minus-5.
At the par-four 12th, Koch hit her approach inside four feet of the hole to stand alone atop the leaderboard at six-under. However, she ran into trouble with a three-putt bogey at the 16th to fall back into a tie for the lead.
Kim joined the leaders at five-under with a seven-foot birdie at the par-four 16th. The 25-year-old took the outright lead at the very next hole after she knocked her nine-iron within 12 feet to complete a bogey-free round.
'She likes this golf course,' said her caddie, Worth Blackwelder. 'She feels very comfortable here, and the golf course sets up well for her game.'
Sorenstam recovered from a bogey at the third with a stretch of three straight birdies from the seventh. At the par-four 11th, Sorenstam hit a sand-wedge 10 feet from the cup for birdie to reach three-under.
The Swede had a chance at eagle at the par-five last but two-putted for birdie to finish two shots off the lead.
'I feel really good,' said Sorenstam, who ousted Karrie Webb in a playoff to win this event in 2000. 'I'm very pleased in the way I'm playing, with the way my season started, and with how I'm playing today.'
Kathryn Marshall, Leta Lindley, Kris Tschetter, Jackie Gallagher-Smith, Akiko Fukushima and Michele Redman finished tied for 11th at three-under-par 69.
Defending champion Rachel Teske got off to a terrible start with a triple- bogey at the par-four first. The Australian added five birdies and four bogeys for a round of two-over-par 74.