Kim, 15 years and five months, became the second youngest champion ever. Tiger Woods was 22 days younger than Kim when the top player in the game won in 1991.
'I can't believe I won this tournament,' said Kim, the second foreign-born winner of the championship.
Chung would have been the youngest ever to hoist the trophy had he prevailed on Saturday, but was happy to take second place.
'I think it was a relief just to get here,' said Chung, 14. 'I think I have a lot more confidence now. I tried my best and as long as I did that, I'm happy.'
Chung actually won the first hole with birdie, but things would not get any better. Kim parred the second to square the match, then holed a 21-foot birdie putt at the fourth to go 1-up.
The pair traded wins at five and six, but it was Chung's cold putter that became the story. He missed a 5-foot birdie putt at the sixth, then an 8-footer for birdie at No. 7.
Kim went 2-up with a win at the ninth, but a Chung birdie at No. 10 closed the gap to 1-down. Kim sank an 18-foot birdie putt at the 12th to reclaim his 2-up advantage, but Chung trimmed the gap with a par at the 14th.
Chung stayed in the match with a 10-foot, downhill bogey putt at the 17th. He missed a 6-foot birdie putt at the last that could have extended the match to extra holes.
'I was expecting David to make his putt and we would have a playoff,' said Kim. 'David's putting was awesome this week. My heart was pounding really hard. I though I was going to have a heart attack.'
Kim received an exemption into the 2004 U.S. Amateur in August at Winged Foot Golf Club plus an exemption from local qualifying for the next three U.S. Opens.