Anand has won the World Chess Championship five straight times but many experts believe Carlsen, 22, has a chance to unseat him, the BBC reported.
The contest is comparable to the face-off between Bobby Fischer and Boris Spassky in Reykjavik, Iceland, in 1972, the BBC said.
The match is being held at the Hyatt Regency in Chennai, the South Indian city formerly known as Madras.
Hundreds of people gathered at the Hyatt to follow the opening game from the lobby, the Press Trust of India reported. Anand and Carlsen are to play 12 games, with the match ending Nov. 29.