In the US, you have sales-tax, which has nothing to do with VAT.
From Europe>non-EU-countries, you export a service.
On export of goods and services, there are no taxes to be levied.
Aah, see, my bookkeeper had told me a while ago that I _had_ to charge VAT. I doubted his response at the time, but when I tried to check it, I couldn't find the rule explicitly stated anywhere. Thanks!