Chávez graduated from Madonna High School in Mesilla. She received her Bachelor's from New Mexico State University and Master's degrees in Theatre from Trinity University whose program was housed at the Dallas Theatre Center. While in college, she began writing dramatic works. Later she entered the MFA program at the University of New Mexico (UNM) and earned a degree in Creative Writing under the direction of mentors Rudolfo Anaya and Tony Hillerman.
In 1986, she published her first collection of short stories, The Last of the Menu Girls. She has received various awards, including the American Book Award, the Premio Aztlán Literary Prize, the Mesilla Valley Author of the Year Award, and the 2003 Hispanic Heritage Award for Literature. Chávez taught at New Mexico State University for various years, eventually moving on to create The Border Book Festival in her hometown of Las Cruces. Currently she is developing, along with her husband, Daniel Zolinsky, a Borderland Art and Resource center, Museo de La Gente/Museum of the people, archiving the history and story of her borderland community.