The South Korean made six birdies en route to a blemish-free 66, which was enough for the outright lead ahead of compatriot and world number one Inbee Park, who led for most of the day before Kim birdied at the 17th.
"This is my first time in U.S. Open and I didn't think that (I'm) going to do it like this," Kim said to www.lpga.com.
Park was the youngest winner of the US Open when she was crowned champion in 2008 and is looking for a clean sweep of major titles this season having already triumphed at the Kraft Nabisco Championship and the LPGA Championship.
A five-under-par 67 keeps her firmly in the hunt and she was quick to send a warning to her rivals.
"I do have a lot of confidence in myself at the moment," Park, who has five victories so far this season, said.
"The way I'm playing, the way things have been going, the way I've been getting the luck, I think I am in the zone. I've been playing my best in my career at the moment. I really just want to enjoy the moment."
Fellow major winner Anna Nordqvist will also feel she is firmly in the hunt on four under par alongside fellow Swede Caroline Hedwall, South Korea's In-Kyung Kim and Lizette Salas of the United States.