Native English Speakers would not use "chamber door" in regular, everyday situations. I probably have not said "chamber door" in my entire life. It is something that one can find in written English (books). The word "chamber" in today's English is very formal, and it is also used only in specialized contexts (chamber musuc, Chamber of Commerce, etc.). And chamber door is even less common.

I agree with the other responses. Unless i"m reading Poe's "The Raven" aloud, I don't think I ever say "chamber-door." http://www.poetryfoundation.org/poem/178713

No, we never use the word "chamber door." I think it's quite old-fashioned, and not in modern usage.