Barua is from Kolkata in the Indian state of West Bengal. In 1978, Barua, as a 12-year-old, became the youngest participant in the Indian Chess Championship. In 1982, Barua defeated the then-world number two ranked Viktor Korchnoi in London. He was awarded the Grandmaster title in 1991 by FIDE, becoming the second Indian to achieve the title, after Viswanathan Anand. In 1983, he won the Indian Chess Championship for the first time. He has since won it twice more, in 1998 and 2001.