To note an apparent oddity where this question is concerned:
He is a Spanish. - incorrect
He is Spanish. - correct
He is a Spaniard. - correct
It seems that other nationalities don't have a word like "Spaniard" in English.
1. I'm a Norwegian. - correct and it sounds "natural".
2. I'm a Chinese. - correct, but does it sound "natural"?
In light of sentence number 1, I can see Gwen's point about "He is a Chinese." quite clearly, yet at the same time, it just doesn't sound "natural" to me. It seems to be a rather odd inconsistency that I had never noticed before.
What about this one? - I'm a French. - I can't say it sounds quite right, yet "I'm a German." sounds fine to me.
"I'm a Swedish." Neither can I say this one sounds right. But this one, "I'm a Russian." sounds fine.
I'd have to say, though, that typically we would not use the indefinite article in this type of sentence.
Interesting inconsistencies we have here. mm....

Oh yes and one more thing, if we say, "I'm a .....................Help! Wait a minute.... :grab: