Heat a grill pan coated with cooking spray over medium-high heat. Place each chicken breast half between 2 sheets of heavy-duty plastic wrap, and pound each piece to 1/4-inch thickness using a meat mallet or rolling pin. Sprinkle both sides evenly with 1/8 teaspoon salt and black pepper. Add chicken to pan, and cook 4 minutes on each side or until done.
While chicken cooks, combine 1/8 teaspoon salt, tomatoes, vinegar, and garlic, stirring with a whisk.
Place buns, cut sides up, on a baking sheet. Broil 1 minute or until lightly toasted. Place 1 chicken breast half on bottom half of each bun. Add arugula to tomato mixture, and toss gently to coat. Arrange about 1/2 cup arugula mixture over each chicken breast half. Cover with tops of buns.