yes you can. i think i may have heard that you need to show your duty orders to show being stationed in va, but don't quote me.
have a look here:
http://leg1.state.va.us/cgi-bin/legp504 ... d+18.2-308
for our cc statutes. section D starts the chp part. section G talks about the safety class requirement. per G5, you may not even need the class.
by statute, the circuit "shall issue" in 45 days, maximum, unless denied for cause. depending on where you are, it can take anywhere from 2 weeks to the full 45 days. there are processes in place to 'pressure' circuits that drag their feet beyond that, if they don't follow statute and certify your app as a temporary permit.
cost is also governed by statute at $50, maximum. some circuits are less, though. the range is $15 to $50.
finally, some circuits require fingerprints for first-time applications, while others do not. that requirement was repealed in the legislature this year and should go into effect on july 1.
hth.