This is India's highest score against any opponent surpassing the previous best of 726/9 declared against Sri Lanka in 2009.
Playing only his third Test, the 25-year-old Nair forged two major partnerships -- 181 for the sixth wicket with Ravichandran Ashwin (67) and then 138 for the seventh wicket with Ravindra Jadeja (51) -- to take India to the record total at the M.A. Chidambaram Stadium here.
Nair has now become only the second Indian batsman to score a triple ton after swashbuckling opener Virender Sehwag, who has two triple tons to his name.
Brief Scores: England 477 vs India 759/9 declared (Karun Nair 303 not out, Lokesh Rahul 199, Parthiv Patel 71).