Preheat the oven to 375-degrees. Cover the bottom of a heavy 6-quart casserole with the celery and onions and add the parsley and tarragon. Place the oil in a shallow dish. Dip the chicken pieces into the oil, coat all sides evenly and place in the casserole. Pour the vermouth over the chicken and sprinkle with the salt, pepper and a few gratings of nutmeg. Tuck the garlic around and between the chicken pieces.
Cover the top of the casserole tightly with aluminum foil and fit the lid over the foil to create an airtight seal. Bake for 1 1/3 hours without removing the cover. Check for doneness; return casserole to the oven if the chicken seems underdone.
Serve the chicken along with the pan juices, the garlic and thin slices of heated French bread spread with garlic squeezed from the root end of the clove.