Federer, who won his 20th grand slam title with his victory at Melbourne Park, was ruthless with his 21-year-old opponent once again on Thursday and took his unbeaten run this year to 16 matches, equalling his record from 12 years ago.
Chung said he had enjoyed going toe-to-toe with Federer in a tight first set.
“I was down one break, and I'm just trying to stay calm and I'm just trying to learn from Roger," the Korean told the ATP's official website. "And I come back, five-all, and he played good. I'm really happy to play against Roger."
Federer will next meet Borna Coric, who defeated world number nine Kevin Anderson 2-6 6-4 7-6(3).
The 21-year-old Croatian had initially looked out-gunned by the big-serving South African, who had won all three of their previous meetings without dropping a set.
After weathering an onslaught of huge serves in the first set, however, Coric was able to force longer rallies in the second and third, where his speed and accuracy allowed him to control points.
“I didn't start very well. He was hitting the ball very big, and I just couldn't find my rhythm on the ball,” Coric said.
“I started going more for the serve. And then I broke him earlier in the second set, which was really helpful.
"In the third, again, I knew it's one break, it's two or three points that are going to decide, and that's what happened.”
The match appeared all but over in the third when a frustrated Coric double faulted to hand Anderson a break for a 4-2 lead but the world number 49 broke straight back and went on to force a tie-breaker.
Anderson was ragged thereafter and Coric pumped his fist in triumph after the seventh seed sent a forehand long to hand the Croatian the biggest win of his career.
(Reporting by Rory Carroll and Shrivathsa Sridhar; Editing by Nick Mulvenney/Peter Rutherford)
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