MacNeille was born May 11, 1907, in New York City and was raised in Summit, New Jersey, the first of two brothers.
At Bailey Island he became acquainted with Frank Aydelotte who encouraged him to go to Swarthmore College from which he graduated with highest honors in 1928.
Following in Aydelotte's footsteps he was a Rhodes Scholar at Balliol College, Oxford, England 1928–1930 receiving a B.A.
During several of the years at Kenyon College he was on leave as Scientific Liaison Officer (1944–1945) and Head of Mission (1945–1946) London Mission of the Office of Scientific Research and Development, American Embassy in London, England.
From 1954–1961 he was professor and chairman of the Department of Mathematics at Washington University in St. Louis, and then from 1961 professor and chairman of the Department of Mathematics at Case Western Reserve University in Cleveland, Ohio, until his death.