1. Rinse chicken and pat dry. Cut into 2-inch pieces and pulse in a food processor until coarsely ground. Transfer to a bowl; season with salt and pepper. With hands, mix in bell pepper, cilantro, and chili sauce until just combined; do not overmix. Form into eight 1/2-inch-thick patties.
2. Preheat grill. Lightly oil rack. Grill burgers on rack over moderate heat 5 minutes. Flip burgers and top each with 1 slice cheese; continue to grill until cooked through, about 5 minutes more. Meanwhile, grill buns, cut sides down, until golden brown, about 1 minute. Arrange burgers in buns with onion and lettuce. Makes 8 servings.