Prepare tartar sauce by stirring together mayonnaise, relish, hot sauce, garlic, and lime juice in a small bowl. Cover and refrigerate at least 20 minutes.
Prepare chicken burgers by mixing together green pepper, red pepper, cilantro, onion, garlic, hot sauce, salt, and pepper in a large bowl. Mix in chicken using your hands until well blended, then sprinkle on bread crumbs, and continue mixing until incorporated. Divide the meat into 8 portions, and flatten to make patties.
Preheat an outdoor grill for medium-high heat and lightly oil grate.
Cook patties on preheated grill until no longer pink in the center, about 5 minutes per side. Assemble burgers by spreading the cut sides of the hamburger buns with tartar sauce, adding a chicken patty, and topping with a piece of lettuce. Voila! You have a tasty Chicken Tartar Burger.
