I'm not at my main computer today so I can't identify the individual file that calls this field, but you should be able to find it using Windows Grep, and search for "country_to_state form-row-first update_totals_on_change country_select" . Chesney hasn't given a URL but looking quickly at mdspharm's link from further up the page...
Unfortunately he has other issues too, in that having added a product to the cart there is no 'go to cart' displayed, so I manually changed the url from .../shop/ to .../cart/ and got to the cart page where the problem displays. There is a piece of text, 'select an option', shown by the country field (or where the country field SHOULD be, if it was visible!) and I don't have that shown on my own checkout page - makes me think he has another script or addon running there, and its this additional script which is introducing the 'display: none;' element thats causing the problem. But maybe I'm wrong and this is just a 'standard' installation.
Anyway, if you look at the source around that field, you'll see
<select name="billing_country" id="billing_country" class="country_to_state form-row-first update_totals_on_change country_select" style="display: none;">
It's the display:none; that you need to track down and eliminate. If you Grep your complete installation you'll find which php file contains the hook, and if there IS a plugin involved here then Grep that too for the same line and you should be able to track it down.
Hope that helps!