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Kalki was born to French parents in a small village in Pondicherry. Her parents had come to India as hippies 38 years ago and settled there after they fell in love with the country. Her parents are devotees of Sri Aurobindo.
Kalki was studying in Ooty when her parents insisted she attend university. Kalki studied drama and theatre in Goldsmiths, University of London, where she also worked with a theatre company called Theatre of Relativity for two years. She performed in various plays like David Hares The Blue Room, Marivauxs The Dispute and a devised play The Rise of the Wild Hunt in her two year stint with the theatre group....debuted in Anurag Kashyap's critically acclaimed 2009 Hindi film Dev.D. She played the character of Chandramukhi in Dev.D, which is a modern take on Sarat Chandra Chattopadhyay's Bengali novella Devdas.