Place the chicken breasts between 2 pieces of plastic wrap and pound to an even 1/8-inch thickness using a meat pounder.
In a large nonreactive skillet, melt 1/2 tablespoon of the butter in 1/2 tablespoon of the olive oil over moderately high heat. Lightly season the chicken with salt and pepper. When the butter stops foaming, add 2 pieces of chicken to the pan and sauté, turning once, until lightly browned and cooked through, 2 1/2 to 3 minutes. Transfer the chicken to a platter and keep warm in a low oven. Heat the remaining olive oil and another 1/2 tablespoon of the butter in the skillet and sauté the remaining chicken; keep warm. Pour off the fat from the pan.
Add the wine to the skillet and boil over high heat until reduced by half, about 2 minutes. Reduce the heat to low and add the lemon zest, lemon juice, capers and half the parsley. Cut the remaining 3 tablespoons cold butter into pieces and whisk them into the sauce.
Transfer the chicken to warmed plates and pour the sauce on top. Sprinkle the remaining parsley on the chicken, garnish with the lemon slices and serve.
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