The 22-year-old led from start to finish and her 21-under-par total of 263 broke the previous record low score by two shots.
It is also one better than the men's majors best of 20 under set by Jason Day at the 2015 PGA Championship
at Whistling Straits and then matched by Henrik Stenson at July's British Open Championship
at Royal Troon.
Chun's four-shot victory from fellow South Koreans Ryu So Yeon (66) and Park Sung Hyun (69) gave the popular LPGA Tour rookie her second major after winning last year's US Women's Open.
That triumph saw her burst into the limelight, not least because of her unusual nickname of "Dumbo"
and her fan club called "The Flying Dumbos" -- who would have been delighted by her magnificent play in golf's newest major.
Since its inception in 2014, Chun is the second South Korean to claim the crown, with Kim Hyo Joo winning in 2014.
She found it hard to come to terms with her triumph after a near flawless round with just a single bogey on the 14th and three birdies to maintain her overnight advantage.
"I just can't believe I have just won the Evian Championship on 21 under. I'm not dreaming am I?" she said.
Chun only joined the LPGA Tour full time this year and is now certain to win this season's Rookie of the Year award.
Another award winner Sunday was world No. 1 Lydia Ko, despite finishing well adrift on two over par after a 73.
She collected the Rolex Annika Major Award for the best overall performance in the five majors, the trophy named after the legendary Annika Sorenstam of Sweden.
Chun also won €440,000 ($487,500) for her sterling efforts, taking the advantage after a brilliant eight-under 63 on the first day.
She has made a fine comeback to the top after a spell out following a bizarre injury sustained at Singapore Airport when fellow player Jang Ha Na's father lost control of a suitcase and it fell down an escalator, striking her.
"After the injury I was struggling with myself and my body and psychological problems," she said. "I was in a bad mood, a negative side."
"But I got my passion back at the Olympics. Making the team was a huge goal and I was so proud to wear the national flag," said Chun, who finished 13th in Rio.