Drake, the eldest child of two American expatriates, was born in Paris, France. Her grandfather, Tracy Drake, and his brother had opened the Drake Hotel in Chicago on New Years Eve in 1920. The Drakes lost their money in the 1929 stock-market crash. As a result, she returned to the U.S. on the SS Île de France with her parents, brothers, and a nanny. She grew up in Chicago, Westport, Connecticut, Washington, DC, Virginia, North Carolina, and New York City. She went to 12 different schools, both private and public, before concentrating on theatre and acting at National Park Seminary.