Chocol studied architecture at the polytechnic in Prague (1908-24), then at the academy in Vienna, under guidance of Otto Wagner (1907-09). He was one of three significant Cubist architects, together with Pavel Janák and Josef Gočár; all three were members of the Mánes Union of Fine Arts.
Three buildings he designed (1913) in Vyšehrad (part of Prague) are considered masterworks of cubist architecture. In 1914 he abandoned the Cubist style and began working in the internationally oriented constructivist style. Most of his other designs (cubist factory, theater) were admired but never realized.
Chochol was also active in politics: he was a founding member of the Left Front organisation and the Association of Socialist Architects, and was the only one of the Czech Cubists with strong political views.