Cook the pasta in salted water according to package directions.
Drizzle the olive oil over the chicken and season on both sides with Cajun seasoning, salt and pepper.
Preheat a grill, grill pan or skillet to medium high heat.
Place the chicken on the grill and cook for 5-6 minutes on each side or until cooked through. Cut the chicken into slices.
While the chicken is cooking, make the sauce.
In small pot, combine the heavy cream, butter and 1/2 teaspoon salt and 1/4 teaspoon pepper over medium-high heat. Bring to a simmer and cook, stirring, until thick enough to coat a spoon, about 4 minutes.
Stir the parmesan cheese into the sauce, cook until melted.
Toss the pasta with the sauce and arrange the chicken on top. Sprinkle with Cajun seasoning, tomatoes, green onions and shredded parmesan, then serve.