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Amilakhvari was born in Bazorkino (now Chermen, North Ossetia–Alania, Russian Federation), where his family had moved from their ancestral estate at Gori, Georgia during the Russian Revolution of 1905. The house of Zedginidze-Amilakhvari had formerly served as hereditary Master of the Horse to the Georgian Crown ("Amilakhvari") and retained their princely dignity during the Imperial Russian rule of Georgia. Dimitri's grandfather, Ivane Amilakhvari (1829–1905), was an eminent general in the Russian army. His father, Colonel Giorgi Zedginidze-Amilakhvari, also served in the Russian military and transferred his loyalty to the short-lived Democratic Republic of Georgia in 1918-21. After the Russian SFSR occupied Georgia early in 1921, the family fled to Istanbul, Ottoman Empire, where Dimitri attended a local British School, and later, in 1922, emigrated to France.