Best way to ask this question of my boss?

I finally found a new job (after much searching) and yesterday was my first day. I’m working for a popular nonprofit organization so the facilities are wonderful but everything isn’t quite up-to-date. Now I’m just going to be honest, the office chair is nasty. I don’t know how old it is and it is quite flimsy. It is, however, usable. What I’d like to do is bring in another one or ask if they have any replacements. I wouldn’t mind saying i have an extra sitting around in my garage. But as I am very new to the job I’m having troubles thinking of the appropriate way to ask the question without sounding nitpicky. Also I think they might be concerned about bringing a new chair in as it is in the middle of a community room (the community room is locked while I’m out of it but it still leaves the chair a bit open for theft and damage). So would you wait to ask? And how would you ask?