Heat skillet over medium heat. Add chorizo and break into chunks with a wooden spoon. Stir until cooked through and lightly browned, about 8 minutes. Remove the chorizo to a plate.
Add onions and bell peppers to the pan juices and cook until tender, about 5 minutes.
Return chorizo to skillet with onions and bell peppers and stir to combine and remove from heat. Add chorizo and vegetables to a oven-safe baking dish.
Sprinkle with cheese. Bake until cheese is bubbling, about 15 minutes.
Garnish with green onions and cilantro. Serve hot with tortilla chips.