No, you only use javascript to submit the selection to the server. After the sumbit, php can process it and pull further information from the database.
So when you submit the country, your php script will retrieve the states/provinces from the database based off the submitted country and you can build the second select box from that info. The same will go for the selected state/province and the retrieval of cities. Throughout the processs, the page will reload itself multiple times, but will add a category each time.
The link mniessen provided is a perfect example of this and is something I will be refering to when the time comes. You should really take a look at it. 🙂