Demonyms for historical neighbours of England have irregular forms when speaking of a particular person from there. Scotland has 'Scot' and 'Scotsman'; Wales has 'Welshman'; Spain has 'Spaniard'. Other countries indeed need a second word, such as 'person' or 'citizen' ('a Chinese' sounds offensive to me; I would say 'a Chinese person' in all cases). The only country I can think of where using a bare demonym is grammatical when speaking of a single person from there is Germany with 'a German' - probably because it has the suffix -man.
Edit: A sibling comment pointed out that 'an American' is grammatical, and thinking about it, I think the suffix -an is what makes bare demonyms grammatical - you can say 'an Angolan', 'a Laotian', 'a Peruvian', 'a Moroccan', etc, but wouldn't say 'a Thai', 'a Swedish', 'a Sudanese', etc.