I think the card case or cigarette case are good guesses. Being a youngster, so to speak, 40, I have no experience with the era that this may be from. 20s(?), 30s(?).

I have been following the chain and my instincts would add though that, from the appearance, I don't think it would have been worn around a wrist. It certainly doesn't look like it would have been comfortable hanging from a wrist. I think the ring at the top indicates that it might have been looped or hung around something. Through a belt or sash or something and worn on the waist. Maybe another chain and hung from the neck but that would involve a lot of jewelry which, I would think would not have been stylish back then. Could also be that a part is missing. Maybe it was hooked to a leather or cloth strap or rope that would have been worn over one shoulder and accross the body. Maybe the ring is so that it could be attached to various belts etc. that would have been coordinated with the outfit. Also, it could have been a little thick to include other things like some mad money for when a young lady may have been stranded after a date and had to call home. It is hard to tell from the picture but I don't sense that it looks thick enough for cigarettes. Although you would know better and I suppose it could. Especially if cigarettes were thinner in those days.