Overnight leader Liselotte Neumann struggled to an even-par 72 and shares third place with defending champion Heather Daly-Donofrio (70) and Hee-Won Han (69). They are knotted at minus-6.
The field for this tournament includes winners from the past four seasons as well as active LPGA Tour and World Golf Halls of Fame members. The participating players own a combined 222 LPGA victories.
Hetherington, an Australian, did not get off to the kind of start one would expect with a 65. She bogeyed her first two holes, but atoned for the errors with an eagle at the par-5 fourth. Hetherington added a birdie at No. 5 to move to 1 under par for the round.
Hetherington's iron game was working late on the front side as she ran home 3-foot birdie putts at eight and nine. Her approach spun back to 5 feet to set up her third birdie in a row at the 10th.
The eight-time winner on the LPGA Tour converted a 6-foot birdie putt at the 12th. For the second time in as many days, Hetherington birdied 15 and 16, but appeared to be in trouble at 18.
Her drive landed left, but Hetherington gave herself a chance to save par. She drained a 15-foot par save to post her 65 and stake her claim to a piece of the lead.
'It didn't feel too easy,' said Hetherington, who posted four top-10 finishes this season. 'I got some good rhythm going and putted great as well today. I made a lot of good putts today.'
Kim had an adventurous front nine with three consecutive birdies out of the gate, but a bogey at four. She recorded her fourth birdie of the round on the fifth, but gave that stroke away with a bogey at No. 6.
Kim rolled in a short birdie putt at the eighth to run the front-nine tally to five birdies, two pars and two bogeys, on both of Magnolia Grove's par-5 holes.
On the 11th hole, Kim sank a 10-footer for birdie to get to 9 under par for the championship. She missed the green short with her second shot at the par-5 16th, but chipped to a foot and tapped in for birdie and a share of the lead.
Angela Stanford carded a five-under 67 and is tied for sixth place with Janice Moodie, who shot a 69 of her own. The duo is knotted at 5-under-par 139.
Kim Saiki (68) joined three American Solheim Cuppers -- Pat Hurst (69), Paula Creamer (70) and Juli Inkster (73) -- in a tie for eighth place at 4-under-par 140.