Why cook onion with chicken? Is it just for taste?
Onion tastes good, especially when caramelized, and since both it and the chicken go on to to be cooked for an extended time in the chili, there's really no food safety concern with cooking them together.

Both contribute to the finished flavor of the dish, and cooking them together saves time. There's no magical interaction between chicken and onion - if there were you'd see the same step in many different types of recipes.