Chung won his first bracelet in 1989 in the $2,000 Limit Hold'em event, winning a $212,000 cash prize in addition to the title. This was in his first cash in a WSOP event.
He won his second bracelet in 1991 in the $5,000 Seven Card Stud event, winning $142,000. He also made the final table of the WSOP Main Event in 1993, which was won by Jim Bechtel. Chung finished in 5th place, winning $72,000.
Since then, he has made numerous cashes and wins in various tournaments, both in the WSOP and in other events. As of 2009, Chung has total tournament winnings exceeding $1,700,000. His 13 cashes at the World Series of Poker make up $590,967 of that total.