Pat the chicken dry with paper towels and season liberally on both sides with salt. Flour each piece in a shallow bowl, shaking off excess flour.
Heat 2 tablespoons of butter over medium-high heat until sizzling hot (but not browned). Toss the chicken into it skin side down and let sear for about 4 minutes or until golden brown. Then flip half way through, cooking another minute on each side.
Remove from skillet with a slotted spoon onto paper towels while you make sauce in same pan by adding lemon juice, capers, pepper and remaining butter (save some for brushing the chicken). Simmer until thickened.