Evgeny Chubarov was born on 1 December 1934 in the village of Lower Bobino, Mechetlinskiy district of Bashkiria (USSR). Artist's passion for drawing and painting appeared in his childhood, under the influence of his father. In 1951, wishing to obtain a more stable and prestigious profession, Chubarov moved to Zlatoust and enrolled at Metal Engraving vocational school there. Within three years, the artist studied jewellery and design of decorative weapons. After graduating Chubarov spent five years serving in the Baltic fleet navy.
In 1959, Evgeny Chubarov went to Saratov, and then to Zagorsk (now — Sergiev Posad), where he worked in the restoration workshop of sculptor Dmitry Tsaplin. In 1963 artist's paintings the „March" and the „Factory Landscape" appeared at the exhibition of young artists in Moscow.
In 1970-80's Chubarov worked on a series of powerful multi-figure ink compositions on paper. On a compositional level they inherit Christ Carrying the Cross by Bosch (1515–1516), the expressionism of Boris Grigoriev in his Faces of Russia (1920–30s) and Pavel Filonov's analytical experiments.
In 1986 Chubarov was admitted to the Union of Artists of the USSR (Artist's Union of USSR). The Soviet part of Chubarov's biography is not rich in external events and does not indicate that the artist tried to gain a foothold within the Underground movement: his name does not appear in the lists of artists trying to exhibit independently.