The South Korean, who began the day at the Congressional Country Club in Bethesda with a three-stroke lead, appeared to have surrendered a third major as she dropped four shots on the front nine.
That allowed Thompson to hit the front and victory seemed hers for the taking but the American, who squandered a winning position at last year’s US Women’s Open, once again unravelled by bogeying four of the last seven holes.
Chun consequently ended up winning by one stroke on five under, despite signing for a three-over-par 75.
Thompson shot 73 and finished in a tie for second on four under with Minjee Lee, who recorded a two-under-par 70.
Thompson looked to have taken firm control when she birdied the 11th to lead by two with seven to play but her problems began with a five at the par-four 12th.
Another bogey followed at the 14th and, although she clawed it back with a birdie three on the 15th, worse was to follow.
She took a six at the par-five 16th after a poor chip and an overhit putt and then dropped another shot on the 17th.
Chun, meanwhile, regained her composure and went back to five under with a birdie at the 16th. That proved enough to keep her one ahead of Thompson and Lee, who had finished strongly with two birdies in her final three holes.
“It just means a lot because I didn’t have any wins for three-and-a-half years,” said Chun at the presentation ceremony.
“My sponsors always believed in me, my family and my coach, my caddy and my fans in Korea, they never gave up on me.”
Northern Ireland’s Stephanie Meadow finished in a tie for 10th on level par after a 74. The English pair of Georgia Hall and Mel Reid finished on two over and four over respectively.
