Place chicken in a large pot and add water to cover (about 3 quarts). Add vegetables and salt and bring to a boil. Reduce heat and simmer until chicken is tender and separates easily from the bone.
Remove chicken from stock and set aside. Reserve stock. Shred or chop chicken. To make the roux, melt butter in a 3-quart saucepan over low heat. Stir in flour and cook for 1 or 2 minutes. Bring 8 cups of reserved chicken stock to a slow boil and gradually stir into the roux.
Simmer until soup takes on a glaze, about 15 minutes. Add pimientos, green pepper, shredded chicken to the stock. Simmer for a few minutes, stirring constantly. Season to taste before serving. Serve in heated bowls.
Recipe Tips
You can use the remaining chicken in casseroles, salads, or sandwiches.