Bring a large pot of salted water to a boil over high heat and cook rigatoni until al dente according to package instructions.

Heat olive oil in a skillet over medium heat, add cubed chicken, and cook until browned and cooked through, about 5 to 7 minutes.

Add diced onion, minced garlic, and sliced bell peppers to the skillet and sauté until vegetables soften, about 3 to 4 minutes.

Sprinkle crushed red pepper flakes into the mixture and cook for 1 minute to release the spice.

Pour in chicken broth, bring to a simmer, and cook for 2 minutes, scraping up any browned bits from the bottom of the pan.

Reduce heat to low, stir in heavy cream, and simmer for 3 minutes until the sauce thickens slightly.

Stir in grated Parmesan cheese until melted and smooth, about 1 minute.

Drain the pasta, add it to the skillet, and toss to coat evenly with the sauce; adjust consistency with a splash of pasta water if needed.