Cook pasta according to package directions; drain and keep warm.
While pasta cooks, cut chicken into bite-size pieces. Sprinkle evenly with 1/2 teaspoon salt and 1/8 teaspoon pepper.
Sauté chicken, onion, red bell pepper, and garlic in hot oil in a large skillet over medium-high heat 5 to 7 minutes. Stir in broth, spinach, and remaining salt and pepper. Cook 4 minutes or until spinach is wilted, chicken is done, and liquid is reduced by one-third.
Add chicken mixture to hot pasta, tossing to combine. Transfer to a serving dish; sprinkle evenly with cheese and parsley.