Arnab Chakrabarty grew up in Mumbai, where his father was a professor of chemistry at the Indian Institute of Technology. His tutelage commenced under the Sarod exponent Brij Narayan, disciple of his father the Sarangi maestro Pandit Ram Narayan and also Ustad Ali Akbar Khan of the Seniya Maihar Gharana. Arnab subsequently trained under Pandit Buddhadev Das Gupta of the Shahjahanpur Gharana.
At the age of 18 Arnab received a Ford Foundation scholarship, which led to a dual degree in ethnomusicology and international relations from Hampshire College in 2002. This experience exposed him to other traditions of music, and led him to experiment with new ideas in sarod construction and design, as well as musical idioms.