Mix salt and pepper together in a small bowl.
Heat the oil and melt the butter in a deep-sided 12-inch saut pan over medium-high heat. (If your pan isn't large enough to hold all the chicken in a single layer, use 2 smaller pans, and put half the chicken, oil, and butter in each one.)
Rub the chicken pieces with the salt and pepper mixture. When the oil is hot but not smoking, use tongs to add the chicken, skin side down. Brown on both sides until the skin becomes beautifully golden brown and the chicken is nearly cooked, about 8 minutes on each side.
Remove the chicken to a serving platter and cover loosely with aluminum foil to keep warm. Pour off about one-half the fat in the pan. Add the shallots to the remaining oil and brown over medium high heat.
Slowly add the vinegar to the skillet and boil until reduced by half. (The fumes will definitely clear your sinuses -- great for a cold!!) Add the crme frache and cook until the mixture is well blended and has turned a nutty brown color, about 5 minutes. Return the chicken to the pan to coat thoroughly and heat briefly in the sauce.
Return to the platter, garnish with parsley, and serve immediately. If there is extra sauce, pass it in a small bowl.
1.Be sure the vinegar has boiled down enough before you add the crme frache or you'll end up with a beige, watery sauce.
2. Brown Chinese vinegar makes a tasty substitution for the red wine vinegar.
Pork Chops in Red Wine Vinegar Sauce: can be made by following the above steps. Unless your chops are very thick, they will not take quite as long to cook as the chicken!
To Freeze: Freeze in freezer safe container.
To Reheat: Heat sauce and chicken in a covered pan until heated through and chicken is cooked through.