Stokes, who took guard at the start of the second day's play after opener Dominic Sibley was dismissed in the last over of the first day, made his unbeaten 63 off 98 deliveries with two sixes and nine fours.
The England big-hitter survived a couple of chances with off-spinner R Ashwin dropping a tough chance off his own bowling and Cheteshwar Pujara dropping him at mid-wicket off the bowling of left-arm spinner Shahbaz Nadeem.
India also wasted a chance to run out Root too as Washington Sundar's throw was wide off the wicketkeeper.
Root built on his overnight unbeaten 128 to rack up his third 150-plus score in succession following his 228 and 186 in Sri Lanka. While he added 28 in the first session with patience, it was Stokes who took on the Indian attack.
Even as lunch approached, the left-handed batsman didn't let up, hitting both Bumrah and Washington Sundar for two fours in an over.
The England skipper had on Thursday pointed out that his side would look to bat till the third day's morning and score 600-700 runs.
As of now, they seem to be on target.
Brief scores
England 355/3 in 119 overs (J Root batting 156, D Sibley 89, B Stokes batting 63, J Bumrah 2/57) vs India
Chennai, Feb 6
England captain Joe Root (batting 156) and all-rounder Ben Stokes (batting 63) added 92 runs in the first session to help England move to 355 for three at lunch on the second day of the second Test on Saturday.
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