Heat the olive oil or butter in a heavy casserole dish. Season the chicken with salt and pepper, then sear until lightly golden. Remove and set aside.
In the same pan, sauté the onion, carrots, celery, and garlic for about 5 minutes until they begin to soften.
Sprinkle over the flour and stir well. Pour in the wine, letting it bubble for a minute as you scrape up all the tasty browned bits.
Stir in the chicken stock, thyme, and return the chicken to the dish. Add potatoes. Bring to a simmer.
Cover and cook gently on the stovetop for 35–40 minutes until the chicken is tender and the potatoes are cooked through.
Adjust seasoning with extra salt and pepper if needed. Serve hot with crusty bread.
