Make the rub: Mix all of the ingredients in a small bowl with 2 teaspoons salt and 1 teaspoon black pepper.
Prepare the wraps: Whisk the mayonnaise and 1 tablespoon of the rub in a bowl. Cover and refrigerate until ready to use.
Preheat a grill or grill pan to medium high. Toss the chicken with 3 tablespoons rub. Oil the grill; grill the chicken until marked, about 6 minutes. Turn and grill until cooked through, about 4 minutes. Transfer to a cutting board.
Wipe the grill clean and brush with more oil. Lay the bread on the grill, then brush with the spiced mayonnaise and top with mozzarella. Grill until the bottom is marked, 1 to 2 minutes. Transfer to a cutting board.
Cube the chicken and arrange down the center of each piece of bread. Top with the tomatoes, onions and lettuce. Roll up and wrap with parchment paper or foil to seal.
Makes 4 sandwiches.