Chemex needs conical filters rather than the Melitta-style ones with a flat edge - similar to the Hario V60, but larger. Also the proprietary Chemex filters are noticeably heavier/thicker, which supposedly gives better results. Those considerations aside, no special reason to use proprietary Chemex filters - I just need to find some the right size. Ebay is not a bad shout, I'll have a look.
I also have a 101 size (single cup) Melitta cone, but getting filters for that has always been a pain - they're widely available in France (or used to be), but have never been common in the UK. A plastic V60 cone is cheap enough, maybe I should just get one of those.
I have the Aeropress too, of course - and a plentiful supply of filter papers for that.
ETA: some online research suggests that Cafec are a good quality alternative brand for filters. Might try those.