The Spanish second seed, who had a walkover in the previous round, had not played since Tuesday and it showed in a dominant 6-3 6-4 6-2 win.
By contrast, Chung had come through three rounds of qualifying and spent nine hours more on court.
Nadal faces Marin Cilic next, while sixth seed Alexander Zverev also won.
Australian 28th seed Nick Kyrgios failed in his bid to progress past the third round at Flushing Meadows for the first time after losing 7-6 (7-5) 7-6 (7-5) 6-3 to Russian Andrey Rublev.
‘Merciless’ Nadal marches on
With defending champion Novak Djokovic and 20-time Grand Slam champion Roger Federer in the opposite side of the draw, Nadal has – on paper at least – a more favourable route to a potential fifth US Open final.
Any concerns over the Spaniard’s fitness after he withdrew from the recent Cincinnati Masters because of fatigue have been dispelled here with two ruthless displays in his two matches.
The 18-time Grand Slam champion did not face a single break point against Chung, who was a top-20 player and Australian Open semi-finalist last year.
He sealed the first set with an ace, the second when he forced the South Korean to hit long and then took victory on his first match point with a rasping forehand winner.
“Nadal is merciless,” former player Jeff Tarango said in BBC Radio 5 Live commentary. “I don’t think I’ve ever seen a human being, animal, or any kind of species, more competitive than Rafa Nadal. Ever. The dude is always competing. He always has to be playing something or winning at something. He never stops.”
Last year Nadal reached the semi-finals here but was forced retire at the end of the second set against Juan Martin del Potro because of a knee injury.
On his way there he had come through two four-setters and a five-setter, which he says took their toll, and so the fact he has reached the second week at Flushing Meadows by spending little more than four hours on court could help him.
Against Chung, he had dispensed with the tape he usually has strapped around his knees.
“The tape is not working any more,” he told the Arthur Ashe Stadium crowd with a smile. “But I’m happy to be playing on the hard court. I’m trying to play a bit more aggressive. I’m happy to be in the fourth round one more time.”
Kyrgios gets his wish to ‘go home’
Kyrgios, 24, led 4-0 in the second set tie-break before 43rd-ranked Rublev fought back to take a two-set lead which he never looked like relinquishing.
Rublev, 21, will meet Italian 24th seed Matteo Berrettini in the last 16 as he looks to further continue a fine North American hard-court swing in which he also beat Roger Federer in Cincinnati.
Kyrgios, who described a line judge as a “whistleblower” for reporting an obscenity the Australian made in the first set, began to lose focus and muttered he wanted “to go home”.
“I guess I’ve been on the road five and a half months now. It’s not easy,” he said afterwards in his post-match news conference.
Kyrgios may get an enforced break as a possible suspension looms following his claims the ATP was “corrupt”.
He later claimed they were not the “correct choice of words” but maintained the governing body was guilty of “double standards”.
The initial comments will be “assessed under the player major offence provision under ATP rules”, with the governing body likely to make a decision after the US Open.
Zverev clocks up the hours to advance
While Nadal is keeping time on court to a minimum, German world number sixth Zverevis racking up the hours.
The 22-year-old, who was taken to five sets in his first two matches, came from behind to beat Slovenia’s Aljaz Bedene 6-7 (4-7) 7-6 (7-4) 6-3 7-6 (7-3) to reach the last 16.
Zverev, who has now played more than 10 hours of tennis and 14 sets over three matches, will face Argentine 20th seed Diego Schwartzman or American Tennys Sandgren next.
“Finally I got some court time,” he laughed after reaching the fourth round at Flushing Meadows for the first time. “I didn’t play that many matches in the summer. Hopefully I can play many more matches here.”
He is joined in the next round by Croatia’s 2014 champion Cilic, who ousted American 14th seed John Isner 7-5 3-6 7-6 (8-6) 6-4 to set up a meeting with Nadal.
Meanwhile France’s 13th seed Gael Monfils is into the last 16 after he beat Canada’s Denis Shapovalov 6-7 (5-7) 7-6 (7-4) 6-4 6-7 (6-8) 6-3 and will play Spaniard Pablo Andujar next.