Heat oven to 400° F. Season the chicken with ½ teaspoon salt and ¼ teaspoon pepper.
Heat the oil in a large skillet over medium-high heat. Working in batches if necessary, cook the chicken until golden brown, 5 to 6 minutes per side.
Reserving the skillet, transfer the chicken to a rimmed baking sheet and bake until cooked through, 15 to 20 minutes.
Meanwhile, in a medium bowl, toss the arugula and beans with the pesto and ¼ teaspoon each salt and pepper.
Add the lemon to the drippings in the reserved skillet and cook until golden, 1 to 2 minutes per side. Mix in the olives. Top the chicken with the olives and lemon and serve with the salad.