It's the first major and sixth career LPGA Tour victory for the 24-year-old South Korean star, who came into the tournament ranked fifth in the world.
Choi shot a 1-over 73 on Sunday and finished at 7 under for a four-stroke victory. Fellow South Korean player Amy Yang had a 71 to finish second.
Choi came into Sunday with a six-stroke lead after shooting a 7-under 65 on Saturday. She got into trouble when she triple-bogeyed No. 10, but recovered to win at the same course where Se Ri Pak won South Korea's first major title in 1998.
Pak was among a group of friends who met Choi after she putted out on the 18th green, showering her with hugs — and victory champagne.
Choi becomes the fourth South Korea player to win the event in the five years, following Inbee Park (2008), Eun-Hee Ji (2009) and So Yeon Ryu (2011).
Choi could afford to have one bad hole Sunday thanks in large part to her remarkable performance Saturday when she had matched the fifth-lowest single round in Open history.
Choi and Yang were the only players to finish the tournament under par.
Sandra Gal of Germany shot a 74 and finished 1 over for the tournament. Il Hee Lee of South Korea, Shanshan Feng of China and Italian Giulia Sergas finished 2 over.
Michelle Wie finished the tournament 10 over. After shooting a 66 on Friday to close with a stroke of the lead, she had weekend rounds of 78 and 80.
Top-ranked Yani Tseng finished 14 over, and still needs an Open victory to complete a career Grand Slam.
The afternoon belonged to Choi, who was even through the front nine, making bogey on No. 1 and making a birdie putt on No. 4.
Then she found trouble.
It started on the par-5 10th hole, when she put her tee shot way left into woods and deep rough. Choi was 8 under at that point — five strokes ahead of Yang, who was 3 under.
After a long delay for a fruitless search for her ball, she went back to the 10th tee with a penalty. Choi wound up with a triple-bogey 8 and appeared to be on the verge of unraveling. Yang made a par on 10, cutting Choi's lead to 2 strokes.
Choi birdied No. 11 but got in trouble again on No. 12, putting her approach shot in the long rough short of the green. She managed to chip out of the rough and hit the green, then rolled in a putt of about 20 feet to save par — and, perhaps, her Open title.
Choi then came within inches of putting her tee shot in the water on No. 13, but her ball bounced to safety and she made another par.
She then made birdies on No. 15 and 16.
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