Chow served as director-general of the Institute of Mathematics, Academia Sinica, and director of the Center of Applied Statistics, Nankai University (Tianjin).
Chow was born in Zhouwan Village, Zhangnan County, Xiangfan, Hubei Province, China.
But because of the Japanese invasion, he left his hometown and finished his high school education in Chongqing - the capital of China during the Second Sino-Japanese War.
He entered the University of Illinois and studied under the guidance of Joseph Leo Doob.
He became a staff member at the IBM Watson Research Laboratory, later at Columbia University till 1962.