'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.

This is a completely puzzling phrase. (The source appears to be a New York Times article, http://well.blogs.nytimes.com/2014/12/23/shopping-for-the-perfect-gift-dont-sweat-it/?_r=0 ) I believe it is some kind of typo or mistake. Tirtho is correct that "firmament" means the dome of the heavens, and it has no other meaning. The writer means something like "Chained firmly to the saying that 'it's the thought that counts.'" Even here, this sounds like a clumsy attempt at metaphor. "Shackled to the idea that 'it's the thought that counts.'" It is hard to believe that the writer doesn't understand the word "firmament" and is using it to mean "firm foundation." I see that the New York Times offers a web page that lets you contact the author, Jan Hoffman, and quite seriously I think you should contact her and ask what she means. Why not? What's the worst that can happen? Look for the link that says "send an email to Jan Hoffman." http://topics.nytimes.com/top/reference/timestopics/people/h/jan_hoffman/index.html