These sandwiches can be prepared the day before and brown-bagged for lunch. The olive salad—which some consider the best part—will moisten the bread overnight.
Combine first 5 ingredients in a bowl; mix well.
Layer bottom half of each roll with 1 provolone cheese slice, 1 ounce chicken, 1 salami slice, and 1 ham slice; top each portion with about 1/3 cup olive mixture and top halves of rolls. Wrap each sandwich tightly in plastic wrap; chill at least 1 hour or overnight. Remove plastic wrap; cut each sandwich in half.