In 1995, Chung played with the San Diego Sockers of the Continental Indoor Soccer League (CISL). He scored twenty-nine goals en route to being named the league's Rookie of the Year. Chung was drafted in the first round (sixth overall) by the Kansas City Wizards in the MLS Inaugural Draft, and finished 1996 with eight goals and nine assists. Chung would be a mainstay at Kansas City for the next two years, was named to his first MLS Best XI in 1997, and would lead all of MLS in games played at the end of its first three seasons, with 97. After 1998, Kansas City traded Chung to the MetroStars, with Mike Ammann in exchange for Tony Meola and Alexi Lalas. He would play with the MetroStars for the next three seasons, but was greatly underused by Metro coach Octavio Zambrano. Chung called the role he played with the Metros an "idiot left wing". He was traded again before the 2002 season, this time to the Colorado Rapids in exchange for a draft pick. Chung was very successful with the Rapids, making MLS Best XI's in both 2002 and 2003. However, with a coaching change to Fernando Clavijo in 2005, he became unhappy, and requested a trade. The wish was granted, as Chung was sent to San Jose for an allocation. In ten years of MLS league play, he scored 61 goals and added 76 assists.
Chung retired after the Quakes moved to Houston after the 2006 season. Upon his retirement, he had played in 278 league matches. In 2008, he played one game with the Treasure Coast Galleons of the Florida Elite Soccer League.