Set aside two 2-quart casserole dishes, or two large disposable freezer containers. (For small families, this recipe will make three or four meals; adjust number and size of pans accordingly).
Skin chicken pieces and remove fat. Sprinkle with salt and pepper.
Add 1 tablespoon olive oil to large frying pan or dutch oven. When hot, add one-half the chicken pieces and brown on all sides. Remove chicken to prepared baking pans and allow to cool.
Add remaining tablespoon of olive oil to the frying pan, and stir in onions and garlic. Sauté over medium-high heat until golden, stirring frequently. Stir in carrots, celery and thyme, and sauté until the vegetables are soft, about 5 minutes. Stir often. Using a slotted spoon, divide vegetables among the casserole dishes or freezer containers; retain juices in pan.
Return frying pan to heat, and add flour. Stir vigorously to blend flour, over medium-high heat, until flour mixture begins to brown. Slowly whisk in chicken broth, white wine and port wine. Stir until boiling and slightly thickened.
Pour sauce over chicken and vegetables. Cover and freeze. Mark containers with recipe name, date of preparation, and these reheating instructions:
Thaw in refrigerator before use. Bake, covered, in 375-degree oven until chicken is no longer pink near the bone, about 1 1/2 hours.
Tip for extended storage: Freeze Chicken Pot-au-Feu overnight in freezer containers slightly smaller than covered casserole pans. When frozen hard, remove from disposable freezer containers and seal using a Foodsaver-brand vacuum food storage bag. Removing all air from the storage bag extends food quality 3 to 5 times.