In a 9-by-13-inch baking dish, whisk together the vinegar, rosemary, garlic, 2 tablespoons of the oil, ½ teaspoon salt, and ¼ teaspoon pepper. Add the chicken and turn to coat. Refrigerate, covered, for 30 minutes.
Meanwhile, in a large bowl, whisk together the mustard, 2 tablespoons of the remaining oil, and ½ teaspoon each salt and pepper. Add the beans, arugula, and onion and toss to combine.
Heat the remaining tablespoon of oil in a large skillet over medium heat. Remove the chicken from the marinade (discard the marinade) and cook until cooked through, 6 to 8 minutes per side. Serve the chicken with the arugula and beans.