He was born in Liverpool, son of a Scottish family doctor and an English mother, and educated at Asheville School, Asheville, North Carolina, Fettes College, Edinburgh, and Christ Church, Oxford.
Gilkey attended elementary school at the University of Chicago Laboratory School, and in 1936 graduated from the Asheville School for Boys in North Carolina.
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A native of Cleveland, Ohio, he graduated from University School in that city, but had completed his first three years of preparatory school at Asheville School in Asheville, North Carolina.