Chun, the 2015 US Women's Open champion, made eight birdies to set the early pace, before Park sank a birdie at the last to match her compatriot.
England's Charley Hull dropped four strokes in the final three holes to end day one at level par.
Hull, 20, did not drop a shot until a triple-bogey six at the 16th.
Laura Davies shot a 69 to end the opening day on two under par, while New Zealand's world number one and defending champion Lydia Ko began with a one-under-par 70.
Thailand's Ariya Jutanugarn closed with a triple-bogey seven on the 18th to fall back to two over par, alongside Scotland's Catriona Matthew.
Chun, 22, told the Ladies European Tour: "Before the round I felt really nervous today and it was windy and there was a thunderstorm this morning, so I tried to focus more on my game.
"I could see the putting lines very well and I was so good rolling the ball on those lines."
Thailand's Ariya Jutanugarn closed with a triple-bogey seven on the 18th to fall back to two over par, alongside Scotland's Catriona Matthew.
Chun, 22, told the Ladies European Tour: "Before the round I felt really nervous today and it was windy and there was a thunderstorm this morning, so I tried to focus more on my game.
"I could see the putting lines very well and I was so good rolling the ball on those lines."
