I just bought a home recently and there is no damper to close off the
chimney. There is a (bird) cap on top, but I want to close off the
whole thing because I don't want my cats climbing up in it.

I need a very cheap and very easy suggestion on how to fix this. I
have considered fireplace doors, but can't afford them right now. I
have no money and no expertise in home improvement.

Any ideas?