The megalithic enclosures of Gobekli Tepe (Urfa, Turkey) are the most ancient stone-built sacred structures known so far, dating back to the 10th millennium BC. The possible presence of astronomical targets for these structures is analysed, and it turns out that they may have been oriented – or even originally constructed – to “celebrate” and successively follow the appearance of a “new”, extremely brilliant star in the southern skies: Sirius.