Keep in mind that "native American" normally refers to indigenous people.

Well, I've known Chinese people who have been here decades and still can't speak very well. It's not only vocabulary and pronunciation and accent... it's also cultural. There are many things that are simply "Western" that people even if they speak different Western languages just kind of "get" that are very foreign to Chinese people. Is it possible? I guess anything is possible. Is it likely? Probably not. 

About the linguistic issues above. A mistake that many Chinese people make is callilng themselves "a Chinese" and we just don't say that. Like Aegis said we say "a Chinese person". You all must be taught to say "a Chinese" in schools or something because it is a very common mistake, so don't feel bad. I don't think I ever talked to a Chinese person who could refer to themselves correctly in English before being corrected on that. 

Another thing is that we say only that we are native English speakers, not native Americans. It is indeed true that the people who lived here before Europeans arrived were the only "natives". When you write Native American (as in the tribes that populated the United States originally) then you need to capitalize both words. We just call ourselves Americans usually and the group of people who had their land stolen from them here... we call them Native Americans. We used to call them Indians but no longer do so. 

To polish your English and sound more like an American I suggest watching a lot of TV, including the commercials. It will help you to understand more about the culture. I also suggest you watch a lot of movies. Then listen to books on tape. The more you absorb about the culture, the better your ability to relate to the American way of being will be.  

I hope that helps. 

@ robert2992 - or maybe someone voted you down because your correction was incorrect, or at least incomplete.

Jill: Can a Chinese speaks English as good as a native American does?

robert2992: Can Chinese speaks English as good as a native American does?

Both are incorrect. Here are some possible correct titles:

Can a Chinese person learn to speak English as well as an American?

Can Chinese people learn to speak English as good as native speakers from the US?

etc

It seems that there should not have been an "a" before Chinese...

You're quite welcome Jill. :D

And Robert... no worries about the thumbs up and down thing. People just go a bit crazy with those and it really means nothing usually. I agree with you that being a native speaker in a language is "almost" impossible to emulate. There really is something about hearing your mother's voice in utero and when you are a baby and having those muscles develop for your language when very young and then taking in all those subtleties of culture and movement and sound before you can speak. Then there is just the shear number of hours a native speaker has heard their language being spoken that for an adult would take decades to get that much full-time practice.

Personally, I think trying to sound or be like a native is an unrealistic goal and also not even really desirable. Foreign accents and manners can be very charming. You will be exotic and interesting if you speak English very well, with an attractive foreign accent and subtle differences to how you perceive the world. Foreigners can be much more appealing than the run of the mill every day person a native would meet. Making yourself sound "lovely" and "interesting" rather than "perfect" or "native" I myself think is a better goal to have. At least I'm hoping that's correct because that's my goal in the languages I'm trying to learn.