Cook Penne according to package directions.
Heat olive oil in a large skillet on Medium heat; add onions and garlic; cook until onions are transparent
Add basil, grilled chicken cut into strips and green peppers
Cook 2 more minutes
Add chicken broth and hot penne to skillet and toss together until all ingredients are evenly coated.
Sprinkle with Parmesan cheese and season with salt and pepper to taste. Serve immediately.