Chung first studied directing at Yale University, then trained as an actor at the Royal Academy of Dramatic Art (RADA) in London and graduated in 2003.

In 2011 she had a recurring role as Vivian, an indentured servant at King Uther’s court who then works as an attendant and messenger for Morgan, half-sister of King Arthur, in the medieval romance drama series Camelot. She appeared in the 2015 British TV series Fortitude as Trish Stoddart.

In 2015 she won the role of Mary Magdalene in the TV series, A.D. The Bible Continues. The show was hailed for its international and multi racial casting and opened to 11 million viewers in April 2015.

In 2017, Chung took on the role of Queen Dido in the Royal Shakespeare Company’s production of Dido, Queen of Carthage by the playwright Christopher Marlowe. She also played Agent Whitman in Absentia and from 2017 to 2019 the Master on the TV series Into the Badlands.

In December 2019, along with 42 other leading cultural figures, Chung signed a letter endorsing the Labour Party under Jeremy Corbyn’s leadership in the 2019 general election. The letter stated that “Labour’s election manifesto under Jeremy Corbyn’s leadership offers a transformative plan that prioritises the needs of people and the planet over private profit and the vested interests of a few.”