The key document to determine whether you qualify or not is the Naturalization Certificate or “lack” of it (the so-called Certificate of Non-Existence).

You have to make sure that your ancestor who was born in Italy did not become a U.S. citizen before the birth of his/her son or daughter in the United States. 

A few years ago, Mayor Vincenzo Tamburi, came up with a bright idea to repopulate the ghost town of San Basile, located on the slopes of Mount Pollino in the province of Cosenza (Calabria). The online initiative was called: "A home in San Basile". He put up for sale about 150 abandoned homes and parcels of land ranging from as little as Euro 5,000 each (about $5,600) to a maximum of Euro 60,000 ($69,000). San Basile was an instantaneous success with buyers from all over the world.