Klatten got off to a strong start, sinking four birdies in a row from the third to the sixth hole before rounding off her front nine with another birdie on the eighth to take the turn in 31.
However, the 30-year-old did not enjoy as much success on the back nine, managing just two more birdies and a registering a bogey on the par-four 11th.
Sitting one stroke back is the American trio of Pat Hurst, Alison Lee and Morgan Pressel, who all hit first-round 66s.
Hurst remained consistent throughout the day and enjoyed a bogey-free round that included five birdies. Like Hurst, Pressel was without a bogey in her opening round and prouduced five birdies, two of which came on the closing two holes.
Lee started off with a bogey, but bounced back with consecutive birdies on the sixth and seventh. The 20-year-old slumped to her second bogey of the day on the par-four 10th, but rallied back once more with birdies on the 11th and 12th and a hat-trick of birdies from the 15th to the 17th.
Perrine Delacour, Jacqui Concolino, So Yeon Ryu and Paula Cremer all hit first-round 67s to sit two shots off the pace.
World number one Lydia Ko did not have much success on Thursday as she mustered two birdies and two bogeys in a round of 71 that sees her sitting five shots back.
Inbee Park, who is ranked second in the world, had a very turbulent round, producing four birdies and five bogeys during her round of 72.
Defending champion Lizette Salas fared no better as she recorded a first round 74, which consisted of three birdies and six bogeys.
Meanwhile, reigning US Women's Open champion Michelle Wie withdrew from the tournament after her first round 78 due to a hip injury.