Preheat the oven to 350°. Season the chicken with salt and pepper and dust with the flour, tapping off the excess. In a large deep skillet or shallow flameproof casserole, melt the butter in the oil. Add the chicken and cook over high heat, turning once, until deeply browned and crusty, 12 to 14 minutes. Transfer the chicken to a large plate and pour off all but 1 tablespoon of the fat.
Add the garlic and carrots cook over low heat until softened, 5 minutes. Add the wine and cook over high heat until reduced by half, 5 minutes. Add the bay, thyme, rosemary, prunes and stock and bring to a boil. Return the chicken to the pan. Transfer to the oven and braise until the meat is tender, 45 minutes longer.
Return the pan to high heat and boil until the liquid is slightly reduced, about 5 minutes. If desired, remove the bay leaf, rosemary and thyme sprigs before serving.