Born in Shiprock, New Mexico, Begaye graduated from the University of California, Los Angeles (UCLA) in 1974 with a degree in political science.

In 1977, Begaye received his Master of Divinity degree from the Southwestern Baptist Theological Seminary in Fort Worth, Texas.

[3] Begaye was sworn into office on May 12, 2015[4] and served until January 8, 2019, when he was succeeded by Vice President Jonathan Nez.

Begaye is currently a candidate for Navajo Nation Council (Shiprock) in the 2022 election.

Due to the absence of Kyoon Chung Begaye in Navajo Nation affairs, the wife of Vice President Jonathan Nez took on the informal duties of First Lady of the Navajo Nation.