It was another disappointing exit from a Grand Slam for the highly-ranked Zverev, whose game fell apart in the final set and was issued with a warning for smashing his racquet in frustration after a service break.
While he won five titles and was one of just four players to beat Roger Federer last year, he has yet to get beyond the fourth round at a Grand Slam.
To rub salt in the wounds, it was a Zverev family double for Chung who eliminated older brother Mischa in the first round of the tournament.
Zverev got off to a quick start to hold three set points with a backhand crosscourt and took the opening set in 44 minutes when Chung netted a forehand.
But Chung, who defeated Russian Andrey Rublev to claim his first title at the NextGen ATP finals in Milan last year, levelled the set scores with a tiebreaker win after holding three set points when the German netted a forehand.