The world No 2 fired a six-under 66 at the first round of the British Open overnight to sit one shot back in second place.
The 18-year-old was the early clubhouse leader at the Trump-Turnberry course before world No 4 Hyo Joo Kim shot a seven-under 65.
A win at a major is the one thing that eludes Ko in her remarkable short career to date. She was the youngest to become No 1 in the world, and youngest to reach one, two and $3-million in career earnings.
The closest she has come was a share of second at the Evian Championship as an amateur in 2013. She was third at the Women's PGA Championship last year but her best finish at the three majors so far this season was a share of 12th at the US Open.
"I don't think too much about records," said Ko who has already said she will retire from golf at the age of 30.
"But my goal is to win one major in my career.
"This was my lowest round in a major so it was a nice solid start. I tried to take advantage of the good weather and the par fives."
Ko had seven birdies and one bogey in her round today with a strong putting game leading the way.
"Hit it pretty solid. If I did miss it, I missed it in the right spots where it wasn't that difficult to get up and down," Ko said.
"I holed a lot of solid putts for par and a couple solid putts for birdie."
Ko shares second with American Cristie Kerr. World No 1 Inbee Park is four shots off the leader following a three-under 69.
Despite the blistering round from South Korean Kim, she was upstaged by Donald Trump.
Kim was midway through the first round when Trump, the American presidential candidate, landed in a private helicopter to begin a two-day visit at the tournament being staged at his resort in western Scotland.
The on-course action was initially a sideshow for Trump, who seized the attention by inviting the media to his hotel near the course to continue his presidential campaign. The Republican eventually watched some golf, although the leaderboard was virtually locked in by then.
