Tschenkéli was born in Kutaisi, the second largest city of Georgia, then part of the Russian Empire. He was a younger brother of the prominent Social-Democratic politician Akaki Chkhenkeli. He studied law and world literature at the University of Moscow from 1913 to 1917. Returning to Georgia after the Russian Revolution of 1917, Tschenkéli obtained, in 1920, a state bursary to continue his education in Germany, where he attended the universities of Halle and Hamburg. The fall of the Georgian republic to the Bolshevik invasion in 1921 precluded his return to the homeland. He lectured at the University of Hamburg and, after the end of World War II, moved to Zürich, where he taught the Georgian and Russian languages. In 1961, he obtained the honorary degree of doctorate from the University of Zürich. Tschenkéli died in Zurich of pneumonia. His grave has been lost.