After reaching his 20th Test ton, Root went on to 128 not out in 197 deliveries. He struck 14 fours and a six. Dom Sibley scored 87 as the pair added 200 runs for the third wicket.
"It is a special hundred, but there's a huge amount of cricket to be played," Root said. "Hopefully this will contribute to a good first-innings total. India made us work hard for the runs."
Root became the ninth batter to score a hundred in his 100th Test, joining compatriots Colin Cowdrey and Alec Stewart.
After winning the toss and opting to bat, Root reached his fifty early in the third session. He was watchful against India's main bowlers but opened up to play attractive shots as the session went deeper.
Using optimal footwork and sweep shots to good effect, Root accelerated after tea and dominated the Indian bowling attack on its home soil.
England crossed 200 in the 74th over. Root and Sibley added 100 off 234 balls.
The Indian bowlers toiled hard but the Chepauk pitch didn't offer much assistance as Root reached his third successive test hundred off 164 deliveries.
At the other end, Sibley occupied the crease for 286 deliveries before India struck late when Jasprit Bumrah (2-40) trapped Sibley lbw with a pinpoint yorker. A tired Sibley unsuccessfully reviewed the decision.
England was 67-2 at lunch, and 140-2 at tea.
The pitch at an empty M.A. Chidambaram Stadium has a sprinkling of grass on it, but it is mostly to bind the surface together than to help out the fast bowlers.
"It is a strong first day for us. The pitch played well, although it had an unusual look. It is on the slower side. I was trying to get used to the surface early on and then with time I found it a bit easier," Root said. "It was a bit of a shame to lose Dom at the end. We wanted to take our partnership as deep as we could."
Sibley and Rory Burns (33) had added 63 runs for the first wicket before India struck twice through Ravichandran Ashwin (1-68) and Bumrah to even out the first session.
England made four changes from its last test against Sri Lanka in Galle. Rory Burns replaced injured opener Zak Crawley and Jofra Archer came in for Mark Wood. Ben Stokes and Ollie Pope replaced Sam Curran and Jonny Bairstow, who have been rested for the first half of this series.
India made three changes from its last test against Australia in Brisbane which capped a 2-1 series win. Skipper Virat Kohli returned to lead the side after a six-week paternity leave for the birth of his first child, a daughter.
The hosts went with three spinners. Washington Sundar retained his spot while left-arm spinner Shahbaz Nadeem came in for pacer Shardul Thakur.
Nadeem was a late inclusion to the India squad after all-rounder Axar Patel complained of pain in his left knee late on Thursday.
Veteran pace bowler Ishant Sharma also returned to the side after missing the Australian series due to injury and rehabilitation.
It is the first time international cricket has returned to India since the coronavirus pandemic began nearly a year ago.