In a large skillet or Dutch oven, saute onion in butter until tender. Remove with a slotted spoon and set aside. In the same pan, brown chicken pieces on all sides. Return onion to pan; add potatoes and carrots. Cover and cook over medium-low heat for 30 minutes or until the vegetables are tender. Stir in cream, parsley, salt, and pepper. Reduce heat. Simmer, uncovered, for 15 minutes or until slightly thickened.