This is the combination of two recipes that our family makes frequently. I like to make extra sauce, though there is usually plenty to go around. It is great served with herbed carrots and new potatoes.
Place the chicken breast halves between sheets of wax paper or plastic wrap and pound with a meat mallet (or rolling pin). You can simply tenderize them, or pound to 1/4 inch thickness, depending on your taste preferences. (Note: the thinner the chicken, the faster it will cook. Keep an eye on your chicken to avoid overcooking it.).
Combine flour, salt and pepper and dredge chicken in the flour mixture, shaking off the excess.
Heat 1 Tbs butter in a frying pan over a med heat. Saute the chicken breasts in two batches, for about 2-3 minutes each side, (longer if thicker than 1/4 inch), or until the chicken is cooked through. Transfer to platter and keep warm in a 200 degree oven.
Add oil, chives, green onion and garlic to pan. Saute for 1-2 minutes.
Add chicken broth, cream, tarragon, lime juice, brandy (if using), and parsley to pan and raise the heat to med-high and cook until the sauce begins to thicken, about 4-5 minutes. Add juices that may have collected around the chicken; stir in the mustard.