Coric, the world number 48, struggled with his first serve and forehand today while Chung was unrelenting in his 6-3 7-5 win over the Croat.
Coric, who struggled with his knee last season, said it was not an issue in today's defeat.
"It was not due to my knee. My serve was off today and I did not play well. I am not surprised with the way he (Chung) played. I knew he was a good player," Coric said after a disappointing start to the new season.
An unforced error by him gave the opening set to Chung. The second set went with serve till 4-4. Coric surged into the lead, breaking Chung in the ninth game. But Chung broke him in his next two games to wrap up the match.
Another qualifier to make the second round was Slovakia's Jozef Kovalik, who sent packing Portugal's Elias Gastao as he rallied to eke out a 6-7(5) 6-4 6-2 win in two hours and 20 minutes.
He next books a match with top seed and tournament favourite Marin Cilic, who had got a bye in his opening round.
Russia's Daniil Medvedev also made it to the next round with a 6-3 6-3 win over Brazilian Thiago Monteiro. Medvedev had rushed to a 4-1 lead in the opening set but allowed Monteiro to trouble him by not containing his unforced errors.
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