I'm a Chinese' doesn't make sense because something is missing. A Chinese what? A Chinese man. 'A'is the indefinite article and needs to be used with a noun. Chinese is not a noun in this case it is an adjective. Chinese is only a noun when it refers to The Chinese (people) or the language.

I am a Chinese.中Chinese是个名词，就是“中国人”的意思，而 I am Chinese.中Chinese是形容词，表示“中国的”。