Chung first studied directing at Yale university, then trained as an actor at the Royal Academy of Dramatic Art in London and graduated in 2003. Her repertoire includes political theatre: Talking to Terrorists, The Overwhelming and Fallujah, as well as classical plays such as Phedre, in which she performed with Helen Mirren, and Epidavros. She has appeared twice in Doctor Who, in one episode playing the Master's assistant Chantho, and in another, a character called the Fortune Teller. Her first film credit was as the voice of Icarus II in Danny Boyle's Sunshine, as well as appearances in In the Loop and Proof. Other television appearances include the drama The Last Enemy and as a reporter in the Sherlock second series episode "The Hounds of Baskerville". 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 romancedrama seriesCamelot. She appeared in the 2015 British TV seriesFortitude 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 the Master on the TV series Into the Badlands from 2017 to 2019.
Activism
Chung co-founded alongside founder Nick Reding the charity SAFE-Kenya which develops theatre for social change in Kenya, focusing on HIV education and abolishing clitoridectomy, and currently sits on its Board of Trustees. She works closely with the charity Peace Direct in support of Envision Zimbabwe, a women's trust that works towards consensus-building and peace in Zimbabwe. She also sits on the RADA Council and British Equity's International Committee for Artists' Freedom. 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."