The restaurant opened in 1963 in a narrow location within the Stater Brothers shopping center on University Avenue. It featured four tables, an eating counter, and a jukebox. Oscar and Josefina Medina, who started the restaurant, named it after the Mexican state of Zacatecas, where Josefina was born. The state also provided the inspiration for her unique recipes, which expanded the menu from the standard American food of the diner that Zacatecas replaced.
The Medinas couldn't afford child care, so their kids would hang out and help out at the cafe after school. They also watched and listened. Soon they amassed stories heard from the varied clientele - statewide and local politicians, blue collar workers, university professors, people from all walks of life - sharing tables and conversations.