In a 4- to 4 1/2-quart slow cooker, combine carrots, celery, wild rice, onion, rosemary, bay leaves, lemon peel, and the 1/4 teaspoon pepper. Top with chicken breast halves. Pour chicken broth over all.
Cover; cook on low heat setting for 6 to 6 1/2 hours or on high-heat setting for 3 hours. Remove chicken and cool slightly. Discard rosemary sprig and bay leaves.
Cut chicken from bone; discard bones. Chop chicken and return to soup along with parsley. Season to taste with additional pepper.