Hitchings, the son of a naval architect, was born in Hoquiam, Washington, and educated at the University of Washington and at Harvard where he obtained his PhD in 1933 and where he taught until 1939. He then moved briefly to the Western Reserve University until in 1942 he joined the Wellcome Research Laboratories where he spent the rest of his career, serving as vice president in charge of research from 1966 until his retirement in 1975.

Hitchings was one of the most productive of modern chemical pharmacologists. He began in 1942 with the study of purines and pyrimidines on the grounds that, as important ingredients in cell metabolism, their manipulation could lead to the control of important diseases at the cellular level. This insight led to the synthesis in 1951 of the purine analog, 6-mercaptopurine (6MP), which, as it inhibited DNA synthesis and thus cellular proliferation, proved valuable in the treatment of cancer, particularly leukemia.

In 1959 6MP was found to inhibit the ability of rabbits to produce antibodies against foreign proteins. A less toxic form, azathioprine or Imuran, was quickly developed by Hitchings and used in 1960 by the surgeon Roy Calne to control rejection of transplanted kidneys.

One further drug was developed from work on 6MP when it was realized that it was broken down in the body by the enzyme xanthine oxydase, the same enzyme that converts purines into uric acid. As gout is caused by an excess of uric acid Hitchings developed allopurinol, which blocks uric acid production by competing for xanthine oxydase.

Other drugs developed by Hitchings include the malarial prophylactic pyrimethamine, or Daraprim, and the antibacterial, trimethoprim. He was awarded the 1988 Nobel Prize for physiology or medicine for his work.