Chun, who won by four shots, broke the record of 20 previously held by Jason Day and Henrik Stenson while the women's record was 19 under.
The 22-year-old was in control from day one and eventually beat compatriots Ryu So-yeon and Park Sung-hyun, who tied for second.
"I just can't believe I won the Evian Championship and made 21 under par," said Chun. "I'm not dreaming, right?".
Chun, who was making her first start after a month out injured, had one bogey on Sunday on the 14th hole, only to move back to 21-under with a birdie on the following hole.
She is the second player, after compatriot Pak Se-ri, to win her first two LPGA titles at major championships.
Defending champion Lydia Ko of New Zealand ended up a disappointing 43rd at two over.
(Writing by Julien Pretot; Editing by Alan Baldwin)
