Elion was born in New York City on January 23, 1918, to parents Robert Elion, a Lithuanian Jewish immigrant and a dentist, and Bertha Cohen, a Polish immigrant. Her family lost their wealth after the Wall Street Crash of 1929. When she was 15, her grandfather died of cancer, instilling in her a Desire to do all she could to try and cure the disease. She graduated from Hunter College in 1937 with a degree in chemistry and New York University (M.Sc.) in 1941, while working as a high school Teacher during day time. Her fifteen fellowship applications were turned down due to gender bias at the time, so she enrolled in a secretarial school, which lasted six weeks before she found a job.