Chandrasekhar was born in Andhra Pradesh, India. Her father Chandrapal (ಚಂದ್ರಪಾಲ್) was an officer in the Indian Army, and her mother Kusuma (ಕುಸುಮಾ) was a home-maker. During her childhood she lived in several towns and cities across India. She is married to H.R.Chandrasekhar, professor of physics and astronomy at the University of Missouri. They have three children.