Sauté onions and celery in butter in a large Dutch oven until tender. Sprinkle 1 tablespoon flour over sautéed vegetables; stir well. Cook over low heat 10 minutes, stirring occasionally.
Add chicken, water, peppercorns, and salt to Dutch oven; bring to a boil. Cover; reduce heat, and simmer 1 hour or until chicken is tender.
Remove chicken from broth; bone, and chop chicken. Strain broth, and discard vegetables. Skim off excess fat. Return chicken and broth to Dutch oven. Combine whipping cream and 1/4 cup plus 2 tablespoons flour; stir into broth. Cook over medium heat, stirring constantly, until mixture is thick and bubbly. Serve immediately over rice.