His father Sir M Ct. Muthiah Chettiar (1887-1929) was a banker who served as a member of the Imperial Legislative Council of India.
Chidambaram Chettiar succeeded his father as a director of the Indian Bank on the latter's death in 1929.
On 10 February 1937, he founded the Indian Overseas Bank, which concentrated on improving the country's industrial sector.
In 1944, with the assistance of Sir C. P. Ramaswami Iyer and British technical expertise, Chidambaram Chettiar founded the Travancore Rayons Limited, with a factory near Perumbavoor.
Chidambaram Chettiar died on 13 March 1954 when the British Overseas Airways flight Lockheed L-749A Constellation, G-ALAM on which he was travelling, crashed at Kallang Airport, Singapore, when it landed short and struck a sea wall after a flight from Jakarta, killing 33 people out of 40 passengers and crew on board.