Chin was born to Peking Opera actor Zhou Xinfang in 1936. She spent her early life in Shanghai and had two short marriages, both of which ended in divorce. Her brother is Michael Chow, owner of the Mr. Chow restaurant chain, and through him, she is the aunt to actress/model China Chow and her brother Maximillian Chow, who are the children of Michael and his late ex-wife, Tina Chow.
She was the first person with Chinese roots to study at the Royal Academy of Dramatic Art, London in 1951 and later became an associate member.
Chin played the part of Liat in the 1950s production of South Pacific in London's west end and moved onto what is probably her best known role, Lin Tang, the diabolic daughter of Dr. Fu Manchu in the Fu Manchu movies starring Christopher Lee. She is also noted for her role as Ling in the James Bond movie You Only Live Twice and in the role of Juicy Lucy in The Virgin Soldiers. She continues to appear in films, including The Joy Luck Club, Memoirs of a Geisha, and the James Bond film Casino Royale. She also has a recurring role in Grey's Anatomy as Helen Rubenstein, the mother of Cristina Yang.