Born in Pishpek (now Bishkek, Kyrgyzstan) to a Russian family. His father served as a military clerk.
In 1918–1919 he studied at the teachers' seminary in Verny under Nikolai Khludov [ru], in 1920–1921 at the art school in Tashkent and in 1924–1930 at VKHUTEMAS (Robert Falk's workshop) in Moscow.
In 1930–1932 he taught at the Institute of Proletarian Fine Arts in Leningrad.
He began as a writer and essayist.
Since 1933, his entire creative life has been connected with Kyrgyzstan. He created an art museum, to the first funds of which the museums of Moscow and Leningrad transferred dozens of works by famous Russian and Soviet artists: Konstantin Korovin, Nicholas Roerich, Vasily Tropinin, Vasily Vereshchagin, etc.
In 1935, an art studio was opened in the republic, on the basis of which an art school was opened in 1939, which today is named after him.[1]
Chuikov's first personal exhibition was held in 1938 in Moscow. He continued to create, and in 1939 the second personal exhibition of his works was held at the House of Writers [ru] in Moscow.
In the 1950–1960s, he traveled to various countries including India, Italy, France, Greece, Bulgaria. From these countries he brought back a wealth of material in the form of various sketches, pencil sketches. Genre paintings and landscapes dedicated to the people and nature of Kyrgyzstan, India (triptych "About the common people of India", 1957–1960).
In 1947–1948 he taught at the Moscow Surikov State Academic Institute of Fine Arts.
Chairman of the Organizing Committee of the Union of Artists of the Kirghiz SSR (1933), Chairman of the Union of Artists of the Kirghiz SSR (1934–1937, 1941–1943). In 1958 he became full member of the Academy of Arts of the Soviet Union. He was a members of the Artists' Union of the USSR.
In 1966, he signed the Letter of the Twenty Five to the General Secretary of the CPSU Central Committee Leonid Brezhnev against the rehabilitation of Joseph Stalin.[2]
He spent the last years of his life in Russia, in Moscow. He was buried at the Kuntsevo Cemetery. He was married to Yevgenia Alekseyevna (1903–1984).[3]