Chakrabarti's writing credits include Red Velvet, a play about Ira Aldridge, an African-American actor at the centre of controversy in 1833 when he takes over from Edmund Kean in Othello at the Theatre Royal in Covent Garden. Premiered in 2012 at the Tricycle Theatre, London, it returned to a sold out run at The Tricycle in 2014 before transferring to St Ann's Warehouse in New York. It returned again to the Garrick Theatre in London's West End as part of Kenneth Branagh's season in 2016. Chicago Shakespeare Theater presented Red Velvet in 2017-18.

Chakrabarti graduated from the Royal Academy of Dramatic Art (RADA) in 1990.

From 1993 to 1996, Chakrabarti presented the BBC children's educational programme Numbertime.

Her theatre credits include The Great Game: Afghanistan for the Tricycle Theatre (2009), Last Seen for the Almeida (2009) (which she co-wrote), Free Outgoing for the Royal Court (2008) and John Gabriel Borkman for the Donmar Warehouse (2007). She is shortly (2017) to appear as Gertrude in a production of Hamlet starring Tom Hiddleston as a fundraiser for RADA.

Chakrabarti runs Lesata Productions with Rosa Maggiora. In 2011, they produced Of Mary, a short film that won the Best Short Film Award at PAFF, Los Angeles 2012. Chakrabarti and Maggiora were nominated for the Best Producer Award at the Underwire Festival, London 2011.

The play won Chakrabarti the Charles Wintour Award for Most Promising Playwright at the 2012 Evening Standard Awards. That same year she was nominated for Best New Play and London Newcomer of the Year at the Whatsonstage Awards. She won the award for Most Promising Playwright at the Critics Circle Awards in January 2013 and was awarded the AWA Award for Arts and Culture that same year. Red Velvet was also nominated for an Olivier Award in 2013 and Adrian Lester was nominated for an Olivier in 2016 for his portrayal of Ira Aldridge in Red Velvet.