Mix broth, carrot, celery, uncooked rice, leek or green onions, dried thyme, and 1/4 teaspoon pepper in a saucepan. Bring to boiling; reduce heat. Cover and simmer 50 or until rice is tender.
Meanwhile, melt margarine or butter; stir in flour. Stir in half-and-half or milk. Cook and stir until bubbly. Cook and stir 1 minute more. Slowly add half-and-half or milk mixture to rice mixture, stirring constantly. Stir in chicken and sherry; heat through. If desired, garnish with carrot peel strips and fresh thyme. Makes 4 servings.