She finished 21 under par, breaking the record of 20 under set by Henrik Stenson at this year's Open and Jason Day at the 2015 PGA Championship.
Chun, who bettered the women's record by two, carded a final round of two-under 69 in France to win her second major by four shots.
"I cannot believe I won and made 21 under par," said the 22-year-old.
Chun, who won last year's US Open, held a four-shot lead overnight and maintained that advantage to win from compatriots So Yeon Ryu and Sung Hyun Park, who tied for second.
She made one bogey on Sunday, but responded immediately at the 15th with one of her three birdies for the day.
The world number seven, who missed the cut last year, then faced a difficult 10-foot putt at the 18th to finish with a two-under-par final round and break the 72-hole record.
England's Jodi Ewart Shadoff carded four birdies but also four bogeys in a final-round 71 to end the tournament tied for 12th on five under.
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South Korea's In Gee Chun shot the lowest ever 72-hole score at a major to win the Evian Championship on Sunday.