Preheat a grill or grill pan.
In a large pot of boiling salted water, cook pasta according to package instructions; drain well.
Heat a nonstick pan over medium heat. Once hot, add the oil. Saute the garlic, peppers, and onion until soft. Then add in the tomatoes and saute for 1 minute more. Stir in the flour.
Stir in the broth, cream, butter, and lemon zest. Bring to a low simmer, stirring occasionally until the sauce thickens and builds flavor. Season with salt and pepper to taste.
Season the chicken on both sides with Cajun seasoning, salt and pepper. Grill the chicken on both sides to an internal temperature of 160 degrees using a thermometer. Set aside to rest for 5 minutes then cut into bite sized pieces.
Toss the pasta in the sauce and serve immediately so the pasta doesnt soak up all the sauce. Garnish with cilantro.