Born in the village of Dubrovka, Kaluga Gubernia, in 1898.
In 1907 he attended an art school for children in Moscow.
In 1918 he moved to Kiev together with his parents.
He attended the Alexandra Exter Studio and the Ukrainian Academy of Arts.
In 1920 Chelishchev left for Turkey, then moved to Berlin in 1921 and on to Paris in 1924.
He did stage design for several productions by Sergei Diaghilev’s Company in Paris.
From 1934 to 1949 he lived in New York.
The Museum of Modern Art of New York staged Chelishchev’s solo show in 1942.
In 1949 he settled in Italy.
Chelishchev did paintings, graphic works and stage design.
Chelishchev died in Frascati, Italy, in 1957.