This is one of the “four quick chicken recipes” that I included in Sara Moulton Cooks at Home. It is a simplified version of a relatively sophisticated dish that used to comprise the whole of my brother Peter’s culinary repertoire. Whenever he confided that he was making Chicken Tarragon for dinner, we knew that things were starting to get serious with whichever young woman he was dating.
Additional kosher salt and freshly ground black pepper to taste
Sprinkle a small amount of water on a large sheet of plastic wrap. Place 2 of the breast halves on top of the plastic and sprinkle again with water. Cover with another sheet of plastic wrap and pound with a rolling pin or meat pounder until about 1/4-inch thick. Repeat with the remaining 2 breast halves.
Mix the flour with the salt and pepper in a shallow pie plate. Heat half the olive oil in a large skillet over medium-high heat until almost smoking. Working in 2 batches, place the chicken in the flour mixture and turn to coat on all sides Shake off the excess flour and add to the skillet. Cook until lightly browned and cooked through, 3 to 4 minutes per side. Transfer to a plate or platter and cover loosely with foil. Repeat with the remaining oil and chicken.
Add the shallots, tarragon, and wine to the skillet. Increase the heat to high and bring to a boil, stirring to pick up any browned bits in the bottom of the pan. Boil until the liquid has reduced to 1 tablespoon. Pour in the cream, bring back to a boil, and boil until reduced by half. Pour in the stock, reduce the heat to medium-high, and simmer for 3 minutes. Season with salt and pepper, reduce the heat to medium, and return the chicken to the skillet. Simmer, turning the chicken often, until warmed through and the sauce is thickened, about 2 minutes. Spoon some of the sauce over each piece of chicken and serve at once.