Cut the chicken breasts horizontally in half to make 4 thinner pieces. Put one piece between two sheets of parchment paper or plastic wrap and use a heavy mallet to pound the breasts into 1/4 to 1/3-inch-thick pieces . Alternatively, you can pound the chicken with the side of a wooden rolling pin.

Season the chicken on both sizes with the salt and a light shower of black pepper. Spread the flour onto a dinner plate.

Set a skillet large enough to hold all of the chicken in one layer over high heat. While that heats up, dredge the chicken in flour, lightly coating each side and gently shaking off excess flour. Pour the oil into the pan ad swirl so evenly coats the pan.

Once the oil is hot, lay the chicken in the pan and cook it on one side until golden brown and the chicken looks cooked around the edges, 1 1/2 to 2 minutes. Turn over and brown the second size for another 1 1/2 to 2 minutes until the chicken is just cooked through. Transfer to a serving plate and reserve in a warm spot in the kitchen, say near the stove.

Into that same skillet, over medium-high heat, melt 1 tablespoon of the butter. Add the shallot and sauté until tender, about 2 minutes. Add the wine and cook for another minute or so. Don't let it boil too rapidly or all of the liquid will evaporate. Add the capers and remaining 1/2 tablespoon of butter, stir and remove from heat.