What to do with your fedora while in a restaurant? An age old question, at least one since hatchecks have gone the way of, well, men regularly wearing fedoras. I submit the following for your consideration:

Your average, run of the mill, over-the-door towel hook.



I haven't field tested this, but as a proof of concept at home it would seem to fit the bill.
Obviously the hook is limited in the thickness of chair, but I've seen similar hooks made of metal that have an adjustable foot that may be wider with the foot removed.
Regards,
Indiana Jeff