Season the chicken breasts with Cajun seasoning on both sides.
Heat olive oil in a skillet over medium heat. Cook the chicken until golden brown and fully cooked, about 6-8 minutes per side. Remove from the skillet and slice into strips.
In the same skillet, sauté the bell peppers until softened, about 3-4 minutes.
Reduce the heat and stir in the heavy cream and Parmesan cheese. Cook until the sauce thickens, about 5 minutes.
Add the cooked pasta and sliced chicken to the skillet. Toss to coat in the sauce. Season with salt and pepper to taste.
Serve immediately, garnished with parsley.