'Firmament' is a Biblical reference where Firmament means the sky, conceived as a solid dome. A SOLID dome, that is unchangeable.
In literature, this term is used to refer to customs, traditions, and beliefs that are taken as axiomatic, and will never undergo any alteration.
When one is chained to the firmament, one is in absolute accordance with such matters. So here, it means, the people that religiously believe that “it’s the thought that counts". By the way, you should've ended the quote before the comma, a mistype I believe. I hope this helped.