Instructions: Rinse chicken and pat dry. Place 1 chicken breast half between 2 sheets of waxed paper or plastic wrap on a sturdy cutting board. With a heavy mallet, pound chicken until it is 1/3 to 1/4 inch thick. Repeat with remaining chicken. (If making ahead, cover and chill up to 4 hours.)

Combine chopped tomatoes, arugula, capers, lemon juice, and olive oil; set aside at room temperature.

In a small bowl, beat the egg with 1 tablespoon water to blend. In another bowl, stir the cornmeal, parmesean cheese, black pepper, and cayenne to blend. Dip each chicken breast half in the egg mixture, turning to coat evenly, then in the cornmeal-parmesean mixture, turning to cover completely.

Place the chicken on a well-oiled barbecue grill (medium heat) (If using gas grill, close lid). Cook chicken until undersides are browned, about 5 minutes. With a spatula, turn the chicken over and cook until browned and meat is no longer pink in center (cut to test), 5 to 6 minutes longer.

Arrange chicken on a serving platter or individual plates; top with tomato mixture and salt to taste.

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