Born in Pittsburgh, Pennsylvania, Cohill received an Artium Baccalaureus degree from Princeton University in 1951 and a Bachelor of Laws from the University of Pittsburgh School of Law in 1956.

[2] On May 4, 1976, Cohill was nominated by President Gerald Ford to a seat on the United States District Court for the Western District of Pennsylvania vacated by Judge Louis Rosenberg.

Cohill was confirmed by the United States Senate on May 18, 1976, and received his commission on May 21, 1976.

He served as Chief Judge from 1985 to 1992, and assumed senior status on November 28, 1994.

He took inactive senior status in 2016, meaning that while he remained a federal judge, he no longer heard cases or participated in the business of the court.