The 20-year-old Jutanugarn, who won the British Open last month, shot a six-under-par 65. Park, who had sat out competitive golf until a few weeks ago to rest her thumb and back, took advantage of calm conditions to fire a five-under-par 66 without a bogey in sight.
"A no-bogey round is a great round. My ball striking was really good, I had a lot of opportunities. The wind wasn't strong so it was a lot easier to play," Park said.
As for Park's thumb, she said it felt much better.
"It almost feels like I don’t want to speak of my thumb again. I want to give it my best this week and injury is not going to be a problem."
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Korea are favourites to make the podium because they have the largest team in Rio, with four competitors in a 60-player field.
In contrast to the men's tournament, all the top women are in Rio competing for the first gold medal in women's golf since 1900.
Lexi Thompson, who had the best round of any American on Wednesday with a three-under-par 68, said: "The Olympics is higher than any major. We have five majors a year and we have one Olympics every four years. I don't think there is a comparison to having a gold medal."
Medals will be awarded on Saturday after four rounds.
(Reporting by Liana B. Baker; editing by Clare Lovell)
