Juan Chávez was born in Colorado of ethnic Mexicans. As a young child, his father died and his family moved from a Colorado mining town to Muleshoe, Texas. In Muleshoe, Chávez remembers facing discrimination and African American children having to go to an African American school. He, as most other ethnic Mexican children in Muleshoe at the time, left school after seventh grade and began working. As a young man, he joined Chicanos Unidos Campesinos, a Muleshoe organization. He also helped lead the Raza Unida Party in the Southern Plains of Texas. He was also a part of the Brown Berets, the UFW, and the Texas Farmworkers Union. He attended demonstrations and marches in various cities like San Antonio, El Paso, Austin, and Washington D.C. with this various parties/groups/organizations. Chavez became the first Mexican American Muleshoe city council member and later the first Mexican American Bailey County Commissioner.