We had a problem with someone in my Sq who had a dual citizenship...I think he had to renounce his non-US citizenship, but I'm not 100% sure. You may want to look into it if it is a factor in your case.
I wasn't born in the US either, so it's nothing to worry about it. Just do your best to include as much info on your application as possible, and be sure not to omit any negative information that may apply...
Cheers! M2