In recognition of the outstanding contribution made by Dr. Gilligan in nuclear science and engineering education, the American Nuclear Society has awarded him the Arthur Holly Compton Award. In a letter of support for the nomination, John Kotek, the Acting Assistant Secretary for Nuclear Energy, wrote:

"Since 2009, Dr. Gilligan has been the driving force within the nuclear energy research community to make the Department of Energy's Nuclear Energy University Programs (NEUP) and complementary Integrated University Program (IUP) and Nuclear Energy Traineeships Program the major successes that they are today. Under Dr. Gilligan's skilled leadership and active, personal stewardship in close collaboration with federal managers, it is no understatement to say that these programs have evolved into the most successful comprehensive research and education programs within the Office of Nuclear Energy (NE)."

The award was established in 1966 in honor of the late Arthur Holly Compton to recognize and encourage outstanding contributions to education in nuclear science and engineering. The award is funded through an endowment by the wife of Edward Malinckrodt, Jr. and by George E. Malinckrodt, and is administered by the Education, Training, and Workforce Development Division (ETWDD).