Chipo Chung was born as a refugee in Dar es Salaam, Tanzania. She is half-Zimbabwean and half-Chinese. Her given name Chipo means "gift" in the Shona language. She spent her first two years in refugee camps in Mozambique with thousands of young people who were escaping the war in then-Rhodesia. Her mother is Fay Chung. Her father is Rugare Gumbo, a long time member of the Zimbabwean government.
Chipo was raised in Harare where she attended Dominican Convent High School and developed her acting with the mixed-race theatre company Over the Edge. At eighteen, she moved to the United States where her mother Fay Chung was working for the United Nations. She studied at Yale University and graduated cum laude with a double major in Theatre Studies and Fine Art.