The Spaniard is looking for a fourth title in New York. Second seeded, he will have as next rival John Isner or Marin Cilic.
He is 7-1 against the American and 6-2 against the Croatian, winner of the tournament in 2014.
Nadal has four breaks on eight occasions. He did not allocate a ball of this kind to Chung, who is 170th at ATP.
"I'm happy to once again enter the fourth round," he told the crowd at the Arthur Ashe Stadium. This court is so unique and special because of the energy generated by the crowd. "