Vialone rice is an Italian long grain rice called "fino" or fine and is used predominantly for risotto. This is the preferred rice for risotto in the Veneto region of Italy as opposed to arborio which is the favorite in most other areas of the country.
In addition to use in risotto this rice is also used in some "thin" soups.
Although white Vialone rice is more typical you can also find brown Vialone rice.
It is typically much harder to find in the U.S. and typically more expensive. You can find it online at Amazon: Campanini Vialone Nano Rice as well as a few other online specialty food stores such as Supermarketitaly.com.