He graduated from De Paul University Law School in 1940 and subsequently worked as a lawyer.

He served eight years during which he was vice chair of the finance committee and president pro tempore.

He sponsored the city's first fair housing law, which passed by four votes.

Opposition to his fair housing activism resulted in his losing a 1966 judicial election, but he became a judge of the Cook County Circuit Court in 1970.

In 1983, when the mayor of Chicago Harold Washington attempted to challenge an opposition bloc made of 29 aldermen, led by Edward Vrdolyak (a conflict that came to be known as the "Council Wars") it was Judge Murray who ruled that the "Vrdolyak 29" had acted legally and that Washington's motion to adjourn the council meeting was improper.