With any POD between 1 AD and 476, have a rump state of the Roman Empire/ Western Roman Empire survive anywhere in Western Europe at least to 1800. Bonus points if the rump state is not Christian or survives to the present day.
Rules are that the state must have continuity of government with the Roman Empire(not just claiming the legacy of Rome), be independent of Byzantium, be a true rump state with limited territory and power(the smaller and more isolated the better), and no ASBs or magic(obviously).
EDIT: Can someone please put this in Before 1900? I put this in the wrong forum, apologies.