1 lb. skinless and boneless chicken breast, cut into 4 pieces
Cooking spray, preferably olive oil
Heat grill to medium-high heat. If using a ridged grill pan indoors, set over high heat until very hot.
In large mixing bowl, combine arugula and spinach. Cover and refrigerate.
In small bowl, whisk lemon juice and salt until salt dissolves. Add ground pepper and whisk in oil until combined. Set dressing aside.
One at a time, place each piece of chicken breast between two pieces of wax paper. Using the flat side of a meat mallet (or bottom of a small, heavy skillet), pound chicken until evenly 1/8-inch thick. If chicken pieces are thick, turning over several times may be necessary. Coat chicken lightly on both sides with cooking spray. If desired, season lightly with salt and pepper.
Grill chicken until white in center, turning it once, about 3 minutes each side.
While chicken grills, pour dressing over greens. Using tongs, turn until well coated. To serve, place one piece chicken on each of 4 dinner plates. Mound 1/4 of salad on top of each.