Ko, who went out in the second group after waking up at 3:30 a.m., was on the 16th hole when the real-estate mogul's helicopter twice circled the Ayrshire links.
"I was like, 'Man, that's a really nice helicopter,"' Ko said. "I would love one."
Ko already was six-under par by then, with a run of four straight birdies from No. 2 giving her momentum. On No. 5, she gripped a 5-wood from 179 yards to inside 2 feet.
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," confessed 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 number one Inbee Park is four shots off the leader following a three-under 69.
Ko held the clubhouse lead for barely an hour before being overtaken by Kim, who rolled in five birdies and an eagle putt from 10 inches at the par-5 14th in her first round in a British Open.