1. Melt the butter with the oil in a large flameproof casserole over medium-high heat. Add the chicken breasts, skin sides down, and cook for 3 minutes, or until golden brown. Turn them over and brown the other sides, about 2 minutes more.

2. Turn the chicken breasts skin sides up, then sprinkle with the shallots, herbes de Provence, garlic, and salt and pepper to taste. Add the stock and wine and bring to a boil. Reduce the heat to low, cover the casserole, and simmer for 25 minutes, or until the chicken is tender and the juices run clear when pierced with the tip ofaknife. Transfer the chicken to a platter and tent with aluminum foil. Boil the sauce over high heat until reduced by about half.

3. Stir in the créme fraîche and chopped tarragon and continue boiling until thickened. If the sauce becomes too thick, add more chicken stock; then adjust the seasoning, if necessary. Coat the chicken with the sauce, garnish with the tarragon, and serve hot.