The world No 2 fired a two-under 69 to sit three shots behind co-leaders Mi Hyang Lee and Lexi Thompson.
Ko had five birdies on the opening day, as well as three bogeys, to finish with a share of 12th.
The 18-year-old is bidding to becoming the youngest ever winner of a major.
The New Zealander can usurp American Morgan Pressel, who won the Kraft Nabisco Championship at 18 years and 10 months in 2007, if successful at the $5.2 million tournament over the weekend.
World No 1 Inbee Park shot a one over 72 while world No 3 Stacey Lewis was a further shot back.