He was born in London, where his father, also a mathematician, was then studying. His family returned to India, where he received his masters degree in 1928 from the Government College in Lahore. In 1931 he received his doctorate from Cambridge University, where he studied under J. E. Littlewood.

Chowla then returned to India, where he taught at several universities. During the difficulties arising from the partition of India in 1947, he left for the United States. There he visited the Institute for Advanced Study for a year or so, then taught at the University of Kansas and at the University of Colorado, before settling at Penn State in 1963, where he remained until his retirement in 1976.

Among his contributions are a number of results which bear his name. These include the Bruck-Chowla-Ryser theorem, the Ankeny-Artin-Chowla congruence, the Chowla-Mordell theorem, and the Chowla-Selberg formula.