The 28-year-old Serb looked as untroubled by the Melbourne heat as he was by the South Korean teenager in the 115-minute contest, charging around Rod Laver Arena and rattling off 40 winners.
World number 51 Chung showed he had some impressive weapons at his disposal, particularly in the opening set, but was not always able to convert his best shots into points.
The 19-year-old stalled Djokovic's progress in an absorbing fifth game of the second set, holding serve after eight deuces, but the five-times champion soon advanced to a second round date with either French teenager Quentin Halys or Ivan Dodig.
(This story has been refiled to change match to game in final paragraph)
(Reporting by Nick Mulvenney; Editing by John O'Brien)
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