In a large skillet over medium heat, cook red, yellow and green bell peppers in 2 tablespoons olive oil with garlic until just tender. Stir in diced tomatoes and diced tomatoes with chiles, reduce heat to medium-low and simmer 10 minutes. Remove to a serving bowl.
Bring a large pot of lightly salted water to a boil. Add pasta and cook for 8 to 10 minutes or until al dente; drain.
While pasta is cooking, heat 2 tablespoons oil and butter over medium heat in a large skillet. Cook chicken in butter mixture until juices run clear, 5 to 10 minutes. Place cooked chicken over tomato sauce and sprinkle with basil, rosemary, thyme, garlic powder and Parmesan. Serve with cooked pasta.