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Chudnovsky received his undergraduate, graduate, and postdoctoral education at Kharkov University in Ukraine, in a school of theoretical physics built by Lev Landau and his students.
During the World War II the institute folded and once again became department of the University of Kharkiv which was evacuated to Kyzylorda in the Kazakh SSR.
After graduation, he was appointed professor of law history at the University of Harkov in Imperial Russia in 1803.