Umesh Yadav (3/83) struck early in the session as West Indies lost their top-order in the first session in which they scored 86 runs.
Chase showed the much-needed application with requisite technique as Indian bowlers struggled after polishing off the top half for only 113 runs.
An hour into the morning session, a man climbed the barricade and sprinted around 70 metres towards Kohli before engaging in a tight hug and then trying to take a selfie with the skipper.
Left-arm wrist spinner Kuldeep Yadav (3/74 in 26 overs) was also impressive during the first two sessions.
Not being able to dismiss the middle and lower-order was a problem in England and it once again turned out to be the bowling unit's bane as the Chase-Holder duo added 104 runs for the seventh wicket.
Chase, along with skipper Jason Holder (52), did enough to ensure that the West Indies will have good first innings total to fight against a heavyweight Indian batting line-up.
Holder finally fell to pacer Umesh Yadav, caught behind by stumper Rishabh Pant.
Chase (98 not out) and tailender Devendra Bishoo (2 not out) were at the crease when the umpires dislodged the bails for the day.