Add the oil, onion, and bell pepper to a large skillet and place it over medium-high heat. Cook 5 minutes, stirring occasionally
Add the chicken to the skillet. Break the chicken apart with a wooden spoon. Cook, stirring occasionally, for 7-8 minutes, until the chicken is cooked through (165 degrees F).
Add the BBQ sauce and tomato sauce to the skillet. Stir to combine. Reduce the heat (low to medium-low) to bring the sauce to a simmer. Simmer for 6-8 minutes, until the sauce thickens.