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 and reserve.
Meanwhile, season chicken with salt and pepper, basil, rosemary, Cajun seasoning, and red pepper flakes. Heat oil in a large skillet over medium heat; add chicken and cook until browned. Remove chicken from skillet and stir in garlic and onions; cook and stir until clear.
Return chicken to skillet over onion mixture and add broth. Simmer until chicken is cooked through and no longer pink inside; spread mixture over pasta and serve.