Stir together 1/4 cup dressing and 2 tablespoons tomato paste in small dish. Pour over chicken in small glass dish; cover. Refrigerate 30 minutes or up to 8 hours.
Meanwhile, stir together drained tomatoes, remaining 1/4 cup dressing, remaining 2 tablespoons tomato paste, onions, basil and garlic. Refrigerate until ready to use.
Preheat grill to medium. Remove chicken from marinade; discard marinade. Grill chicken 10 to 12 minutes or until no longer pink in centers (165 degrees F), turning once. Just before chicken is done, grill bread 2 minutes on each side or until toasted. To serve, place bread on serving plates; top with chicken and tomato mixture.