Brown chicken in 1/4 cup butter in a large Dutch oven. Add water, and simmer 1 hour or until chicken is tender. Remove chicken from broth and set broth aside. Remove meat from bones; cut into 2-inch pieces, and set aside.
Melt remaining butter in Dutch oven; stir in flour. Cook over medium heat, stirring occasionally, 10 minutes or until roux is the color of a copper penny. Stir in remaining ingredients; simmer for 10 minutes. Add chicken and reserved broth; cook over low heat 30 minutes or until vegetables are tender.