Split and butterfly the chicken: Starting on the fat side of the chicken breast, cut horizontally across the breast but not all the way through. Open it up like a book. Pound the chicken 1/8 to 1/4 inch thick.
Place a serving platter or large plate in the oven and preheat to 250 degrees .
Heat a large skillet over medium to medium-high. Season the chicken with salt and pepper and dredge in flour, shaking off the excess. Pour 1 or 2 tbsp. EVOO into the preheated skillet, two turns of the pan. Working in batches, brown the chicken lightly on each side, adding more EVOO as necessary. Transfer to the warmed platter, cover with foil, and keep warm while you make the lemon-butter sauce.
Melt the butter into the drippings. Add the lemon slices and lightly brown. Add the garlic and stir 1 minute. Add the capers. Deglaze the pan with the wine and add the lemon juice and the parsley. Slide the chicken back into the pan and coat with the sauce. Return the chicken to the platter and drizzle with the pan sauce. Serve with slices of the warm bread.