Elion was born in New York. Elion wanted to pursue a job in science. Although women had a hard time getting a job in science during the Great Depression. Elion started as a cancer researcher in high school. She worked as a lab assistant, food analyst, and high school teacher for several years. While Elion worked, she earned her Master's degree at night. In 1941, she earned her M.S. (Master’s in science) degree in chemistry from New York University.