Thousands of people took to the streets to celebrate Thursday's stunning semifinal success over Germany and the Juventus defender is now praying that the Azzurri can overcome defending champion Spain in Sunday's final in Kiev.
"We are there; so close to the cup," Chiellini told Rai Sport. "We want to win to keep this dream going for our fans. We want to give them something big."
Italy was written off by many pundits before the tournament because of the disruption caused by the Scommessopoli match-fixing scandal, as well as its shocking 3-0 defeat by Russia in its final warm-up fixture.
Even Chiellini admitted that the players have been taken back by how far they have come in such a short space of time, pointing out that they could easily have routed a heavily-fancied Germany side.
"Who would have believed such an incredible ride 10 days ago?" the versatile center back exclaimed. "We could have won 3-0 and nobody would have been able to say anything."
While Italy lost to Spain on penalties in the quarterfinals of Euro 2008, the Nazionale have a good record against La Roja in international competition. However, history will have no bearing on Sunday's final, as far as Chiellini is concerned.
"Tradition and statistics count for little now," he declared. "But we believe we can win the European Championship and we want it, while appreciating that Spain are a great team."
Italy's clash with Spain will get under way at 2:45 p.m. ET.