In 1940, Chung graduated from the Department of Mathematics of the National Southwestern Associated University, where he later worked as a teaching assistant.

In 1944, Chung was chosen to be one of the recipients of the 6th Boxer Indemnity Scholarship Program for study in the United States.

Chung's dissertation was titled “On the maximum partial sum of sequences of independent random variables” and was under the supervision of John Wilder Tukey and Harald Cramér.

He then transferred to Stanford University in 1961, where he made fundamental contributions to the study of Brownian motion and laid the framework for the general mathematical theory of Markov chains.

In addition, Chung also explored other branches of mathematics, such as probabilistic potential theory and gauge theorems for the Schrödinger equation.