Begin by bringing a large pot of salted water to a boil. Once boiling, add the penne pasta and cook according to package instructions until al dente, usually about 8-10 minutes. Stir occasionally to prevent sticking.
Once the pasta is cooked, drain it in a colander and set it aside. Make sure to reserve a bit of the pasta water in case you need to thin out the sauce later.
In the same pot, add the prepared Alfredo sauce, the chopped roasted red bell pepper, and the precooked chicken pieces. Heat over medium heat, stirring gently until everything is warmed through and combined.
Once the chicken and sauce mixture is heated, add the drained pasta to the pot. Toss everything together until the pasta is well coated with the creamy sauce. If the sauce is too thick, add a splash of the reserved pasta water to achieve your desired consistency.
Season the pasta with salt and pepper to taste. Stir in the chopped fresh basil just before serving to add a refreshing touch.
Spoon the pasta into bowls and sprinkle with the Parmesan cheese. Serve immediately.