Kvitsiani was born in 1961 in the village of Chkhalta, part of the predominantly ethnic Georgian Svan upper Kodori valley in the then-Soviet Abkhazia, an autonomous republic within the Georgian SSR. He finished the Novosibirsk Institute of National Economy and later graduated the Kiev General Staff Academy with honors. According various reports, he had a criminal record during the Soviet period. A detailed academic study claims he developed contacts to Soviet organized crime while in jail, and that after his release he was involved in running illegal casinos in Abkhazia.