In a large bowl, combine the chutney, yogurt, curry powder, oil, lime juice, salt and pepper. Whisk until combined.
Add the garbanzo beans, goat cheese, green onions, mint, chicken, raisins, hot sauce, if using, lettuce and apples.
Spoon the filling into the center of each wrap, leaving a 2- to 3-inch border. Fold the bottom flap of the wrap up and over the filling. Fold in the sides and roll up tightly to enclose the filling. Cut each wrap in half and serve.