Add the onion, carrot and garlic to the skillet and cook over moderately low heat, stirring, until softened, about 8 minutes. Add the wine and cook until nearly evaporated, scraping up any browned bits stuck to the pan, about 5 minutes. Add the stock and bring to a boil. Nestle the chicken and thyme into the broth and cover tightly. Transfer to the oven and cook for about 1 hour, until the chicken is very tender.