Place an oven rack about 6 inches from heat and preheat the broiler.
In a medium bowl, whisk the eggs with the pepper until well-combined, then set aside.
In an 8-inch ovenproof skillet, heat the oil over medium heat. Once hot, add the onions and peppers, then cook for 3 to 5 minutes, stirring frequently, until the vegetables have softened.
Stir in the chicken, then pour in the eggs. Tilt the pan to distribute the eggs evenly.
As the eggs begin to set on the bottom, use a spatula to lift the mixture and tilt the pan so the uncooked portion can flow underneath.
When the eggs are about halfway cooked, sprinkle the mozzarella on top and spoon on the sauce. Remove from heat.
Place the skillet in the oven and broil until the top is set, the eggs are cooked, and the cheese has melted, about 5 minutes.
Remove from the broiler and let the frittata sit for at least 5 minutes before slicing.