Pound chicken breasts on a work surface using a meat mallet or heavy pan to 1/4-inch thick.
Whisk vinegar, lemon juice and olive oil in a bowl and add the chicken breasts. Marinate for 15 minutes.
Heat a cast iron skillet/grill pan or a nonstick pan on the stove over a medium high heat. Gently place chicken breasts in the pan and let cook for about 3-4 minutes each side until cooked through.
Meanwhile, in a separate bowl, whisk the pesto, olive oil, vinegar, salt and pepper. Add arugula, salami and black olives. Toss together.
Place chicken breast in the center of a large plate, Add a nice handful of the dressed arugula on top. Serve.
