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Yes you Can once you get your certificate you can apply online before coming here.
they are always looking for teachers who can teach English.

Before you commit money to that course let me recommend that you take the CELTA course in Chicago at Teaching House or in Vietnam, at either Apollo or ILA.  I say this not because I think it is absolutely needed but because you will be going against the prejudices of those doing the hiring and they will prefer the CELTA.  There are advantages to taking the course in Vietnam.  One is money.  It is about $1K less.  Also ILA has a package that includes lodging if you are not inclined to live with relatives who might have financial expectations.  If you do not have any prior teaching experience, the CELTA gives much more hands on experience with students than other courses and in Vietnam the students will of course be Vietnamese.  Another real advantage is that you can start looking for employment from "on the ground," while still in the course.

As absurd as it might seem to you and I, you might also consider taking the IELTS test to prove your fluency.  Don't take it cold though but learn about the test, as even native speakers can get less than perfect scores, particularly in writing.  It is not unheard of for native speakers to take the test, particularly IELTS instructors. 

I have an acquaintance who, although born in Vietnam, was a graduate of Michigan State University, worked as a legal translator for an Australian law firm downtown, and still received lower teaching wages than native speakers and even other Europeans.  His grammar was essentially native although he had a very, very slight accent.  He has moved on to more lucrative pursuits but this is what you are up against. 

All said, despite the absurd prejudices you will face, you should go ahead with your plans.  With some basic Vietnamese, you should have a good foundation to become modestly fluent rather quickly which will hugely, to borrow a currently popular word, enhance your outside of school life.     I'm sure you know that I am not just talking about ordering noodles.

One last caveat.  I see you are just out of school, so I assume you do not have a big nest egg.  Be sure you arrive with at least a few thousand US$ and a credit card for a plane out in case things really don't work out.  Also check out other threads and sites for the documents you will need for your work permit.  Personally, I recommend certifying and translating everything in Vietnam rather than through the Viet embassy in DC.  Good luck.

Edit:  Just came across this.  I hope the moderators will let the link stand as I don't think the topic is really well covered here as this is a more general expat forum. 

THIGV is right when he says there is a bias against Vietnamese Americans or "viet kieu".  I'm a Vietnamese American and have worked in Vietnam as a teacher for over 10 years.  Many English schools want native english teachers who are "white" even though a native english speaker is anyone whose first language is English regardless of ethnicity.  I suggest knowing the average hourly rate for foreign teachers for the city you plan to work in because they will low ball you and also don't speak Vietnamese during your interview. Good luck in your job search.

Thanks for the reply!

I was just wondering, what was the job search like for you?

I've also seen the average salary is between $1,500 to $2,000. But since I'm a Vietnamese/American,  would you know what the expected salary would be?

Let me know!

Kenny