Bring a large pot of lightly salted water to a boil over high heat. Add the rigatoni pasta and cook until al dente, 8 to 10 minutes; drain and keep warm.
Heat the olive oil in a large frypan over medium-high heat. Season the chicken with salt and pepper and cook in the hot oil until lightly browned on all sides and no longer pink in the center, about 7 minutes. Remove the chicken from the pan and keep warm.
To the frypan add the onion, garlic and chillies. Cook and stir until the onion has softened, about 4 minutes. Add the roasted red capsicums and crushed tomatoes. Bring to a simmer then stir in the heavy cream and cooked chicken. Simmer 2 or 3 minutes then stir in the pasta. Sprinkle with Parmesan cheese to serve.