Born in Kutaisi in the family of the writer Davit Chkheidze (he would be executed during the Great Purge in 1937), Chkheidze studied acting at Tbilisi State Institute of Theatre from 1943 to 1946 and continued his education under Sergei Yutkevich and Mikhail Romm at VGIK in Moscow from 1949 to 1953.

He rose to fame with Magdana's Donkey, co-directed with Tengiz Abuladze, which won the Best Fiction Short award at the 1956 Cannes Film Festival.

[5] During the Soviet era, Chkheidze was a Communist Party member[6] and also served as secretary of Georgian SSR Union of Cinematography, then a top decision-making body in the field, from 1963 to 1981.

[7] He was appointed executive director of Georgia's Kartuli Pilmi studio in 1973, a position he held, intermittently, into the 1990s.

[8] A star in his honor was opened by Georgia's Ministry of Culture in front of the Rustaveli Cinema in Tbilisi in 2013.