Rice was born Elmer Leopold Reizenstein in New York City on September 28, 1892. He was the son of Jacob Reizenstein and his wife Fanny (neé Lion), German-Jewish immigrants. Jacob Reizenstein worked as a traveling salesman and bookkeeper but suffered from epilepsy and had problems finding employment. This situation contributed to Rice leaving high school while he was still a sophomore to seek employment. He worked in several office jobs, which left him unhappy. After spending a year at a law firm, Rice decided to pursue a legal career to support himself, though he was not particularly interested in the law.

To that end, Rice passed a state exam that gave him the equivalent of a high school diploma, then entered New York Law School in 1910. During the long legal classes, Rice would read plays to relieve his boredom. He had been a fan of the theater...