A son of Korean immigrants, Chung had a humble upbringing on a small farm in rural Arkansas, which later influenced his life-changing decision to pursue a career in filmmaking. He attended Yale University, where he majored in Ecology, but during his senior year, Chung decided to deviate from his initial plan to attend medical school and instead enrolled in the University of Utah's film program.
Earning his Master of Fine Arts degree in 2004, Chung's first film, Munyurangabo, premiered at the 2007 Cannes Film Festival, receiving widespread critical acclaim. Variety praised the film as "an astonishing and thoroughly masterful debut," while American film critic Roger Ebert called it "a beautiful and powerful film - a masterpiece." Chung's subsequent film, Lucky Life, was developed at the Cinefondation at the Cannes Film Festival and premiered at the 2010 Tribeca Film Festival and 2010 Torino Film Festival.
Today, Chung resides in Brooklyn, New York, with his wife Valerie. In 2007, he collaborated with local filmmakers in Rwanda to establish Almond Tree Films Rwanda, a successful film production company and academy that has made a significant impact in the region.