Chakrabarti was born to Hindu-Bengali parents in the suburb of Kenton in the London Borough of Harrow. Her father, a bookkeeper, has been cited by Chakrabarti as an influence on her gaining an interest in civil liberties. She attended Bentley Wood High School, a girls’ comprehensive school, then Harrow Weald Sixth Form College. Chakrabarti was an active member of the Social Democratic Party from 1985 to 1987.
She studied Law at the London School of Economics, at one point acting as a research assistant to Leonard Leigh who wrote a paper on the British approach to terrorism and extradition; the paper was published in early 1997. After graduating with a Bachelor of Laws, Chakrabarti was called to the Bar by the Middle Temple in 1994. In 1996, she started working as a barrister for the Home Office.