Chandrasekhar was born on 19 October 1910 in Lahore, Punjab, British India (now Pakistan) in a Tamil Brahmin family, to Sitalakshmi (Divan Bahadur) Balakrishnan (1891–1931) and Chandrasekhara Subrahmanya Ayyar ( (1885–1960) who was stationed in Lahore as Deputy Auditor General of the Northwestern Railways at the time of Chandrasekhar's birth. He had two elder sisters, Rajalakshmi and Balaparvathi, three younger brothers, Vishwanathan, Balakrishnan, and Ramanathan and four younger sisters, Sarada, Vidya, Savitri, and Sundari. His paternal uncle was the Indian Physicist and Nobel laureate C. V. Raman. His mother was devoted to intellectual pursuits, had translated Henrik Ibsen's A Doll's House into Tamil and is credited with arousing Chandra's intellectual curiosity at an early age. The family moved from Lahore to Allahabad in 1916, and finally settled in Madras in 1918.

Chandrasekhar was tutored at home until the age of 12. In middle school his father would teach him Mathematics and Physics and his mother would teach him Tamil. He later attended the Hindu High School, Triplicane, Madras during the years 1922–25. Subsequently, he studied at Presidency College, Madras from 1925 to 1930, writing his first paper, "The Compton Scattering and the New Statistics", in 1929 after being inspired by a lecture by Arnold Sommerfeld. He obtained 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, Cambridge, secured by R. H. Fowler with whom he communicated his first paper. During his travels to England, Chandrasekhar spent his time working out the statistical mechanics of the degenerate electron gas in white dwarf stars, providing relativistic corrections to Fowler's previous work (see Legacy below).

Chandrasekhar had published around 380 papers in his lifetime. He wrote his first paper in 1928 when he was still an undergraduate student about Compton effect and last paper which was accepted for publication just two months before his death was in 1995 which was about non-radial oscillation of star. The University of Chicago Press published selected papers of Chandrasekhar in seven volumes.

Chandrasekhar developed a unique style of mastering several fields of physics and astrophysics; consequently, his working life can be divided into distinct periods. He would exhaustively study a specific area, publish several papers in it and then write a book summarizing the major concepts in the field. He would then move on to another field for the next decade and repeat the pattern. Thus he studied stellar structure, including the theory of white dwarfs, during the years 1929 to 1939, and subsequently focused on stellar dynamics, theory of Brownian motion from 1939 to 1943. Next, he concentrated on the theory of radiative transfer and the quantum theory of the negative ion of hydrogen from 1943 to 1950. This was followed by sustained work on hydrodynamic and hydromagnetic stability from 1950 to 1961. In the 1960s, he studied the equilibrium and the stability of ellipsoidal figures of equilibrium, and also general relativity. During the period, 1971 to 1983 he studied the mathematical theory of black holes, and, finally, during the late 80s, he worked on the theory of colliding gravitational waves.

Chandra worked closely with his students and expressed pride in the fact that over a 50-year period (from roughly 1930 to 1980), the average age of his co-author collaborators had remained the same, at around 30. He insisted that students address him as "Chandrasekhar" until they received their Ph.D. degree, after which time they (as other colleagues) were encouraged to address him as "Chandra". When Chandrasekhar was working at the Yerkes Observatory in 1940s, he would drive 150 miles to and fro every weekend to teach a course at University of Chicago. Two of the students who took the course, Tsung-Dao Lee and Chen-Ning Yang, won the Nobel prize before he could get one for himself. Regarding classroom interactions during his lectures, noted Astrophysicist Carl Sagan stated from firsthand experience that “frivolous questions” from unprepared students were “dealt with in the manner of a summary execution”, while questions of merit “were given serious attention and response”.

In his first year at Cambridge, as a research student of Fowler, Chandrasekhar spent his time calculating mean opacities and applying his results to the construction of an improved model for the limiting mass of the degenerate star. At the meetings of the Royal Astronomical Society, he met E. A. Milne. At the invitation of Max Born he spent the summer of 1931, his second year of post-graduate studies, at Born’s institute at Göttingen, working on opacities, atomic absorption coefficients, and model stellar photospheres. On the advice of P. A. M. Dirac, he spent his final year of graduate studies at the Institute for Theoretical Physics in Copenhagen, where he met Niels Bohr.

After receiving a bronze medal for his work on degenerate stars, in the summer of 1933, Chandrasekhar was awarded his PhD degree at Cambridge with a thesis among his four papers on rotating self-gravitating polytropes, and the following October, he was elected to a Prize Fellowship at Trinity College for the period 1933–1937.

During this time, Chandrasekhar made acquaintance with British Physicist Sir Arthur Eddington. In an infamous encounter at the Royal Astronomical Society in London in 1935, Eddington publicly ridiculed the concept of the Chandrasekhar limit. Although Eddington would later be proved wrong by computers and the first positive identification of a black hole in 1972, this encounter caused Chandrasekhar to contemplate employment outside the UK. Later in life, on multiple occasions, Chandrasekhar expressed the view that Eddington's behavior was in part racially motivated.

Chandrasekhar married Lalitha Doraiswamy in September 1936. He had met her as a fellow student at Presidency College, Madras. Chandrasekhar was the nephew of C. V. Raman, who was awarded the Nobel Prize for Physics in 1930. He became a naturalized citizen of the U.S. in 1953. Others considered him as warm, positive, generous, unassuming, meticulous, and open to debate, as well as private, intimidating, impatient, and stubborn regarding non-scientific matters, and unforgiving to those who ridiculed his work.

In January 1937, Chandrasekhar was recruited to the University of Chicago faculty as assistant professor by Otto Struve and President Robert Maynard Hutchins. He was to remain at the university for his entire career, becoming Morton D. Hull Distinguished Service Professor of Theoretical Astrophysics in 1952 and attaining emeritus status in 1985. In 1953, he and his wife, Lalitha Chandrasekhar, took American citizenship. Famously, Chandrasekhar declined many offers from other universities, including one to succeed Henry Norris Russell, the preeminent American Astronomer, as Director of the Princeton University Observatory.

During World War II, Chandrasekhar worked at the Ballistic Research Laboratory at the Aberdeen Proving Ground in Maryland. While there, he worked on problems of ballistics, resulting in reports such as 1943's On the decay of plane shock waves and The normal reflection of a blast wave. Chandrasekhar's expertise in hydrodynamics led Robert Oppenheimer to invite him to join the Manhattan Project at Los Alamos, but delays in the processing of his security clearance prevented him from contributing to the project. It has been rumoured that he visited the Calutron project, where he suggested that young women be employed to operate the calutrons producing enriched radioactive materials for the atomic weapons.

From 1952 to 1971 Chandrasekhar was Editor of The Astrophysical Journal. During the years 1990 to 1995, Chandrasekhar worked on a project devoted to explaining the detailed geometric arguments in Sir Isaac Newton's Philosophiae Naturalis Principia Mathematica using the language and methods of ordinary calculus. The effort resulted in the book Newton's Principia for the Common Reader, published in 1995. Chandrasekhar was an honorary member of the International Academy of Science.

Chandrasekhar did some work at Yerkes Observatory in Williams Bay, Wisconsin, which was run by the University of Chicago. After the Laboratory for Astrophysics and Space Research (LASR) was built by NASA in 1966 at the University, Chandrasekhar occupied one of the four corner offices on the second floor. (The other corners housed John A. Simpson, Peter Meyer, and Eugene N. Parker.) Chandrasekhar lived at 4800 Lake Shore Drive after the high-rise apartment complex was built in the late 1960s, and later at 5550 Dorchester Building.

Chandrasekhar was awarded the Nobel Prize in Physics in 1983 for his studies on the physical processes important to the structure and evolution of stars. Chandrasekhar accepted this honor, but was upset the citation mentioned only his earliest work, seeing it as a denigration of a lifetime's achievement. He shared it with william A. Fowler.

Once when involved in a discussion about the Gita, Chandrasekhar said, "I should like to preface my remarks with a personal statement in order that my later remarks will not be misunderstood. I consider myself an atheist." This was also confirmed many times in his other talks. In an interview with Kevin Krisciunas at the University of Chicago, on 6 October 1987, Chandrasekhar commented: "Of course, he (Otto Struve) knew I was an atheist, and he never brought up the subject with me".

Chandrasekhar's most notable work was the astrophysical Chandrasekhar limit. The limit describes the maximum mass of a white dwarf star, ~1.44 solar masses, or equivalently, the minimum mass which must be exceeded for a star to ultimately collapse into a neutron star or black hole (following a supernova). The limit was first calculated by Chandrasekhar in 1930 during his maiden voyage from India to Cambridge, England for his graduate studies. In 1979, NASA named the third of its four "Great Observatories" after Chandrasekhar. This followed a naming contest which attracted 6,000 entries from fifty states and sixty-one countries. The Chandra X-ray Observatory was launched and deployed by Space Shuttle Columbia on 23 July 1999. The Chandrasekhar number, an important dimensionless number of magnetohydrodynamics, is named after him. The asteroid 1958 Chandra is also named after Chandrasekhar.

After his death, his widow Lalitha Chandrasekhar made a gift of his Nobel Prize money to the University of Chicago towards the establishment of the Subrahmanyan Chandrasekhar Memorial Fellowship. First awarded in the year 2000, each year, this fellowship is given to an outstanding applicant to graduate school in the Ph.D. programs of the Department of Physics or the Department of Astronomy and Astrophysics.

Chandrasekhar died of a sudden heart attack at the University of Chicago Hospital in 1995, having survived a prior heart attack in 1975. He was survived by his wife, Lalitha Chandrasekhar, who died on 2 September 2013 at the age of 102. In the Biographical Memoirs of the Fellows of the Royal Society of London, R. J. Tayler wrote: "Chandrasekhar was a classical applied Mathematician whose research was primarily applied in astronomy and whose like will probably never be seen again." He was a serious student of literature and western classical music.

On 19 October 2017, Google showed a Google Doodle in 28 countries honouring Chandrasekhar’s 107th birthday, and the Chandrasekhar limit.