Barry was born in County Mayo, Ireland and immigrated to the United States in 1907 with his parents, Thomas J. and Catherine J. (Hennelly) Barry, who settled in Queens County, New York. He attended public schools and graduated from New York University in 1925 and from New York University School of Law in 1929. He was admitted to the bar in 1929 and commenced practice in New York City. He married Emily B. La Mude on February 7, 1934.
