Yes, you may OC without any kind of permit. There are no laws or regulations that prevent you from OCing as a non-resident. (I am assuming that you are legally allowed to possess a firearm)
Do you have a North Carolina permit? If so, it is valid in VA. If not, there are a few benefits to having a permit so you may want to look at obtaining a non-resident permit if you so choose.
I also recommend that you check out the Virginia Citizens Defense League. It is a great group dedicated to gun rights in VA. If you go to their website you can sign up for VA-ALERT (on the right side of the page) which is a free email system that will keep you informed about everything gun-related going on in the state. The website is http://www.vcdl.org
You may also wish to check out the following links for places where you can and cannot carry.