The LPGA event is run each season by retiring Annika Sorenstam.
Webb's round featured an eagle at the par-five third hole and five birdies.
Kim bogeyed No. 4, but three birdies on the back nine and eight birdies in all helped her grab a share of the lead through 18 holes.
"When you have as many chances as I did today, even though you feel like you could have left some out there, I'm not going to complain too much," Webb said when discussing her round.
"I saw the lines very well today and I had a lot of opportunities," Kim said.
Sophie Gustafson is third at 6-under 66.
Seven golfers share fourth at 5-under 67.
Sorenstam, the world's second-ranked women's player, is locked in a tie for 60th place at even-par 72.