The Kiwi sits two shots behind playing partner Shanshan Feng of China, who shot a bogey-free 6-under 66.
Ko was six-under with five holes to play before dropping two more shots.
Despite complaints over playing the biggest event in women's golf on a course owned by President Donald Trump, there were no apparent protests Thursday over his comments about women.
The road outside the club was relatively traffic free and there was no sign of protesters.
Feng has played on the LPGA Tour since 2007. She started her round on the 10th hole and played the back side in 5 under, rolling in five birdies. She added another at No 1 and then parred her last eight holes.