India were 39 for one at stumps on the fourth day of the first Test here at the MA Chidambaram Stadium after England set them a target of 420 runs to win.
India, who lost the wicket of Rohit Sharma early, need a further 381 runs while visitors England need nine wickets.
Sharma was bowled by left-arm spinner Jack Leach for 12. Cheteshwar Pujara (batting 12) and Shubman Gill (batting 15) were at the crease.
The highest successful chase for India is 406/4, way back in 1976 in the West Indies. India had also chased 387 against England in 2008 in Chennai.
Earlier, India off-spinner R Ashwin took six wickets for 61 runs as England were bowled out for 178 in their second innings an hour before close.
After dismissing India for 337 in the first innings in first session and gaining a 241-run first innings lead, England added to their lead through the day.
England skipper Joe Root once again top-scored with 40 while Ollie Pope (28), Jos Buttler (24) and Dominic Bess (25) too made significant contributions.
While Ashwin took 6/61 for his 28th five-wicket haul, left-arm Shahbaz Nadeem took two for 66. Pace bowlers Ishant and Jasprit Bumrah took one wicket apiece.
Ishant became the third Indian pacer and the six Indian bowler to get to 300 Test wickets when he got rid of Daniel Lawrence.
Earlier in the morning session, India added 80 runs to their overnight score of 257/6 before getting bowled out.
Brief scores: England 578 and 178 (Joe Root 40, Ollie Pope 28, D Bess 25, J Buttler 24; R Ashwin 6/61) India 337 all out and 39/1 (India trail by 381 runs).
