In that particular instance, using "a Chinese" alone doesn't sound natural, just as using "an English" alone in the same type of sentence doesn't sound natural. I think this is because "Chinese" and "English" can be seen as being nationalities/groups of people and also languages.
By the same token, if someone were to say "I am a Venezuelan.", it would sound better. Or "I am an American."
It depends on what the specific sentence is.
Does everyone know what I mean?
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