Whisk together lemon juice, shallot, olive oil and black pepper in a large baking dish. Add the chicken, turn to coat and marinate in the refrigerator for 30 minutes.
Preheat grill to high. Remove chicken from marinade, season with salt on both sides and grill for 2 to 3 minutes per side or until golden brown and just cooked through.
Combine arugula, tomatoes and onions in a large bowl, toss with the vinegar and oil and season with salt and pepper, to taste. Place each paillard on a large plate, drizzle with extra-virgin olive oil and top with some of the arugula-tomato salad. Garnish with lemon halves.