The 18-year-old has never missed an LPGA cut, but a bogey, a double bogey and a triple on Tuesday left her nine shots off the pace set by Juli Inkster, Cristie Kerr and Sydnee Michaels.
Coming off victory at last week's Swinging Skirts Classic, Ko would have been feeling confident as she began her round in Irving, and she started in solid fashion, taking the turn in 34. However, six dropped shots in three holes from the 14th to 16th sent the New Zealander crashing down the leaderboard.
It all started to go wrong for Ko on the 14th as her second shot went past the green before nestling behind a tree. The teenager looked to play over the tree but failed to clear it. She was handed a drop for an unplayable lie and stumbled to a triple bogey.
Matters only deteriorated on the 15th, with Ko finding the water before dropping a further shot on the 16th.
The leading trio had no such problems, with Kerr, Michaels and Inkster sitting on five-under after rounds of 66.
Kerr notched up seven birdies and two bogeys on the day in a round in which she made the most of friendly greens, requiring just 24 putts. Michaels, who like Kerr needed just 24 putts in her opening round, produced a bogey-free round as she goes in search of her first LPGA title. The 54-year-old Inkster produced six birdies and a single bogey.
Angela Stanford, Lexi Thompson, Natalie Gulbis, Maria Hernandez, Ryann O'Toole, Karine Icher, Sandra Gal, Gerina Piller, Wei-Ling Hsu and Alena Sharp find themselves clumped together one shot back after rounds of 67.
Michelle Wie and Mirim Lee are two of the eight players a further shot adrift, while defending champion Stacy Lewis is three shots off the pace after firing a 69.