For the chicken: In a large nonstick skillet, heat the oil and butter over medium-high heat. In a medium bowl, mix together the flour, 1/2 teaspoon salt, and 1/4 teaspoon pepper. Season the chicken on both sides with salt and pepper and dredge in the flour mixture. Shake off any excess flour and cook the chicken until golden and cooked through, 3 to 5 minutes each side. Remove to a plate and tent with foil to keep warm.
For the sauce: Heat the same pan used to cook the chicken over medium-high heat. Add the tomatoes, olives, capers, wine, and lemon zest. Scrape up the brown bits that cling to the bottom of the pan with a wooden spoon. Cook until the tomatoes start to soften, about 4 minutes. Stir in the parsley and season with salt and pepper, to taste.
Arrange the chicken on a platter and pour the sauce over the top.
Recipe courtesy of Giada De Laurentiis