"I am Chinese" is a grammatically correct sentence simply using the adjective "Chinese" to describe yourself. "I am a Chinese" is grammatically incorrect. You could say, "I am a Chinese person" or "I am a Chinese citizen." The reason why you need a noun such as person or citizen in this case is because you used the article "a" before "Chinese." This implies that there will be a noun used in the sentence and there is not. You must insert a noun (such as person, woman, citizen, etc) or eliminate "a" from your sentence. Hops this helps!

It is the difference between Chinese as a citizen of the People's Republic of China and being Chinese as an ethnic member. (Think of those genetically Chinese who live in Singapore, Malaysia, Philippines, Canada and the US.)

Chinese is both a noun and adjective http://dictionary.reference.com/browse/chinese Define: Chi·nese: [chahy-neez, -nees] –Noun . . . . . 4. a native or descendant of a native of China. –Adjective 5. of or pertaining to China, its inhabitants, or one of their languages.