Chandrasekhar (Chandra) was born in Lahore, British India, into a Tamil Hindu family, the third of ten children to Sita Balakrishnan, and Subrahmanya, a senior officer in the Indian Audits and Accounts Department. Subrahmanya was posted in Lahore as the Deputy Auditor General of the Northwestern Railways at the time of Chandra's birth. His mother tongue was Tamil.
Chandra's father was also an accomplished Carnatic music violinist who had authored several books on musicology. His mother was devoted to intellectual pursuits and had translated Henrik Ibsen's A Doll's House into Tamil. She is credited with arousing Chandra's intellectual curiosity early on. Chandra's father's brother, physicist C. V. Raman was a Nobel laureate in physics.
Chandra was tutored at home initially through middle school and later attended the Hindu High School, Triplicane, Madras, British India during the years 1922-25. Subsequently, he studied at Presidency College, Chennai from 1925 to 1930, obtaining his bachelor's degree, B.Sc. (Hon.), in physics in June 1930. In July 1930, Chandrasekhar was awarded a Government of India scholarship to pursue graduate studies at the University of Cambridge, where he was admitted to Trinity College and became a research student of Professor R. H. Fowler. On the advice of Prof. P. A. M. Dirac, as part of his graduate studies, Chandra spent a year at the Institut for Teoretisk Fysik in Copenhagen, where he met Prof. Niels Bohr.
In the summer of 1933, Chandrasekhar was awarded his Ph.D. degree at Cambridge, and the following October, he was elected to a Prize Fellowship at Trinity College for the period 1933-37. During this time, he made acquaintances with Sir Arthur Eddington and Professor E. A. Milne.
In September 1936, Chandrasekhar married Lalitha Doraiswamy, who he had met as a fellow student at Presidency College, Madras, and who was a year junior to him. In his Nobel autobiography, Chandrasekhar wrote, "Lalitha's patient understanding, support, and encouragement have been the central facts of my life."