Cook fettuccine to desired doneness as directed on package. Drain; cover to keep warm.
Meanwhile, heat oil in large nonstick skillet over medium heat until hot. Add chicken; cook 10 to 15 minutes or until chicken is fork-tender and juices run clear, turning once. Remove chicken from skillet; cover to keep warm.
In same skillet, combine garlic, zucchini and bell pepper; cook and stir 4 to 6 minutes or until vegetables are crisp-tender. Stir in Alfredo sauce; cook 1 minute or until sauce is thoroughly heated.
To serve, spoon sauce mixture over cooked pasta. Slice chicken; arrange over sauce. Sprinkle cheese over chicken; sprinkle with pepper.