The Irate Chef is a very minor character in The Emperor's New Groove.
He used to work at a jungle restaurant named Mudka's Meat Hut, until Kuzco kept asking him about "anything special on the menu," and Kronk asked him about "special orders." This is where the chef finally reaches his breaking point and he quits his job in a rage, stating that there was "no respect for anyone with vision." He then storms away, leaving Kronk to cook the meals himself, temporarily. This doesn't help either, as Kuzco and Yzma wouldn't make up their minds about their orders, so the first chef must have quit in perfect timing. Eventually, Kronk rejoins Yzma in their hunt, and it's unknown what became of the restaurant afterwards.