Remove all fat and white tendon from chicken. Flatten slightly between sheets of wax paper with rolling pin. Sprinkle with salt and pepper.
Boil cream in medium-sized saucepan until reduced to 3/4 cup, about 20 minutes. Cream will be very thick.
Heat butter in large skillet. Add chicken pieces, 3 at a time, cooking 3 to 4 minutes on each side. Don't over cook. Remove and keep warm until all chicken is done.
Add chicken broth to skillet. Boil until reduced to 1/4 cup. Stir in pickles, cream, and mustard. Reheat, but don't boil. Add tarragon, parsley and chives. Return chicken to pan just to reheat. Turn to coat with sauce.
Good with buttered zucchini and carrots! Serves 6.