Gronk -- Leads 'Free Brady' Chant ... In S. Carolina Nightclub

More footage from Rob Gronkowski's rager in South Carolina ... this time, he was leading a "Free Brady" chant in the middle of the nightclub ... without his shirt on.

Gronk was in Trio nightclub in Charleston this weekend ... where he started his evening in a button down collar shirt ... before stripping down to a tank top ... before losing his top completely.

And when the toplessness began, so did his vocal support for Tom Brady -- and we're told the entire club followed his lead and joined the chant ... including the chick Rob motorboated earlier in the evening.

Good times.