Chung took up tennis as a way to try to help maintain his eyesight after requiring glasses at a young age. He won the Eddie Herr International and Junior Orange Bowl Boys under-12s titles in December 2008, and was subsequently signed, along with his brother Chung Hong, to the Nick Bollettieri Tennis Academy at IMG in Florida. He began competing on the ITF junior tour in 2012, and was runner-up in the 2013 Wimbledon Boys' Singles, a month after winning his first Futures title. He later competed in his first ATP tournament, the Malaysian Open, being defeated in the first round. He reached a career junior high of No. 7, with an 84–32 win–loss record.
