As a baby, Hector's parents were Mexican illegal immigrants who moved to the United States so that Hector could have a better life. Louis hired Hector as the chef for Cattleman's, and Hector accepted work for very little pay and allowed Nancy to keep all tips from customers.
In Pilot, Louis compliments and approves of Hector's culinary work, claiming that the restaurant's food is fine at the time Jessica started trying to find reasons and/or scapegoats for why the restaurant didn't have a successful beginning. The series would later on prove that the restaurant needed to do better on recognition, not Hector's work.
Hector finally has an episode of his own in Season 3, Citizen Jessica. When California Proposition 187 popped up, Jessica aggressively supported and treated it as if it's already the law rather than a proposition, much to both Louis and Hector's disdain. Angered over Jessica's support for voting "YES" on 187, which he considered an act of racism against Hispanics, Hector and his friends or brothers or cousins (all Hispanics) made a peaceful protest. They chanted "NO ON 187!" alerting Louis that this was disturbing the peace at his restaurant. Jessica proudly called the I.N.S. to intervene and arrest Hector, but they also arrested Jessica herself since she turned out to have overstayed her visa. Thanks to Jessica and the I.N.S., Hector decides that America hates him, quits his job as chef at Cattleman's and makes plans to return to Mexico. Louis scolds Jessica for her racist behavior towards Hector, and while Jessica does apologize, she defends she simply overstayed her visa, while Hector never had one to begin with.