Cook the rigatoni pasta according to package instructions until al dente. Drain and set aside.
In a large skillet, heat the olive oil over medium heat. Add the chicken pieces and cook until browned and cooked through. Remove the chicken from the skillet and set aside.
In the same skillet, add the diced onion and sliced bell peppers. Cook until softened, about 5-7 minutes. Add the minced garlic and cook for an additional minute.
Stir in the crushed tomatoes and heavy cream. Bring the sauce to a simmer and let it cook for about 5 minutes.
Add the cooked chicken back to the skillet and season with salt, pepper, and red pepper flakes if using. Let the sauce simmer for another 5-10 minutes to allow the flavors to meld together.
Add the cooked rigatoni pasta to the skillet and toss everything together until the pasta is well coated with the sauce.
Stir in the grated Parmesan cheese until melted and fully incorporated.
Serve the Chicken Riggies hot, garnished with chopped parsley. Enjoy!