Grammatically speaking, we can answer "She is Chinese" to the question "What nationality is she? or What is her nationality?". But can we also answer "She is a Chinese (girl)" to the question?
Both are technically correct, but using Chinese as a noun is not very common, and doesn't sound right to me (native American English speaker). Saying someone is "a Chinese" sounds quite jarring, describing someone as "a Chinese person", or simply "Chinese" sounds much better.
For many nationalities, this distinction doesn't exist. For example, it's fine to say "he's Italian" or "he's an Italian". For some nationalities, there entirely different words for the adjective and noun - "he's Spanish" vs. "he's a Spaniard". For some nationalities, the noun form doesn't sound right - "he's Japanese" sounds much better than "he's a Japanese".