 Born in Baltimore, Maryland, Murray was raised mostly by her maternal grandparents in Durham, North Carolina. At the age of sixteen, she moved to New York to attend Hunter College, graduating with a Bachelor of Arts degree in English in 1933. In 1940, Murray sat in the whites-only section of a Virginia bus with a friend, and they were arrested for violating state segregation laws. This incident, and her subsequent involvement with the socialist Workers'Defense League, led to a career goal as a civil rights lawyer. She enrolled in the law school of Howard University, where she also became aware of sexism. She called it "Jane Crow", alluding to the Jim Crow racial segregation laws. Murray graduated first in their class, but was denied the chance to do post-graduate work at Harvard University because of her gender. She earned a master's in law at University of California, Berkeley, and in 1965 she became the first African American to receive a Doctor of Juridical Science degree from Yale Law School.
