The 17-year-old, who opened with a two-under par 69, carded a three-under par 68 in round two to climb to a share of sixth place.
The LPGA Tour rookie will begin the third round overnight (NZT) only five shots back from American Brittney Lincicome (65) who leads by one shot on a 10-under par total.
Lincicome held the 36 hole lead at the Wegmans LPGA Championship on her way to losing to Inbee Park in a playoff. She is hoping to be better for that experience but is mindful of the stress of closing it out.
"I really, one of these days, would love to win a golf tournament by like five or 10 strokes, so when I am walking down 18 I can be all smiley and waving and having a good time and not like super stressed ready to like explode inside. That's my next goal, to win a tournament by a bunch of strokes. The pressure is difficult to handle."
Meanwhile, Ko was steady as chases history. The runner-up at Evian last year as an amateur made the turn in one-under par after two birdies and a bogey.
She mixed a birdie and a bogey in her opening nine holes of the back nine before making back to back birdies on 16 and 17 to remain in contention.
The three-time LPGA Tour winner comes into the Evian tournament after a two-week break from the game to allow her wrist injury time to heal.
If she was able to win this week, Ko would become the youngest major winner in history and also world No 1 for the first time.
It is 146 years since Young Tom Morris upset his father to win the Open Championship in 1868 and become the youngest major winner in history at the age of 17 years, five months and eight days.
