Looking through old office drawers that are no longer in use and were left unopened for many years, I found the object pictured. It was empty. Looking at it I figured it must be an old cigarette case. However, it would be weirdly spaced in contrast to other cases I have seen, and the way it is sewn makes the sixth compartment at the bottom virtually useless. Since it is pretty old I thought if anyone can confirm my guess, it's probably you guys.
(EDITED TO ADD—Oops...Ruth was speedier on the draw) I don’t know what you mean by “the sixth compartment at the bottom,” but I suspect it may have been part of a manicure set, as here...
I think the OP means the section that is too flat to hold a cigarette - but it would hold a nail file.