In a large heavy nonreactive skillet, melt the butter in the oil. Season the chicken pieces with salt and pepper. Add them to the skillet skin side down and cook over moderately low heat, turning once and shaking the skillet often, until cooked, about 30 minutes. Transfer the chicken to a platter.
Discard all but 1 tablespoon of the fat from the skillet. Add the garlic, shallot and dried herbs and cook, stirring, until barely soft, about 1 minute. Add the vermouth and boil, scraping up any browned bits from the bottom of the skillet, until reduced to a thick glaze. Add the stock and cook, stirring to reduce slightly, 2 to 3 minutes. Add any accumulated chicken juices to the skillet, then strain the sauce. Stir in the chives and parsley and season with salt and pepper. Spoon the sauce over the chicken and serve.