Add shallots to the same skillet and sauté briefly. Add vinegar and boil until reduced to glaze. Stir in broth. Return chicken, skin side up to skillet. Reduce heat to medium-low, cover and simmer until cooked through, about 10 minutes more. Transfer chicken to serving plates. Add fresh tarragon to liquid in skillet. Increase heat to medium-high, and boil uncovered until liquid is slightly reduced. Spoon sauce over chicken and serve.