Cooking over high heat without stirring gives the chicken and peppers a smoky, charred crust.
Stir together 1 tablespoon lime juice, 1 tablespoon oil, and 1 tablespoon chili garlic sauce in a small bowl. Set aside.
Heat a large cast-iron skillet over medium-high. Working in batches, add pitas to skillet, and toast until lightly browned, about 1 minute per side. Cut in half; set aside.
Increase heat to high. When skillet starts to smoke, add remaining 1 tablespoon oil. Add chicken in a single layer, and cook, undisturbed, until browned, about 1 minute. Stir and cook until browned on both sides, about 1 more minute. Move chicken to sides of skillet. Add bell pepper, and cook, undisturbed, until slightly charred, about 2 minutes. Add zucchini to bell pepper, and cook 1 minute. Add scallions, salt, pepper, and sauce mixture; stir together, and cook 1 minute.
Stir together sour cream, remaining 1 tablespoon lime juice, and remaining 1 1/2 teaspoons chili garlic sauce. Fill each pita half with 1/4 cup lettuce and 1/2 cup chicken-and-vegetable mixture. Drizzle with sour cream sauce, and serve immediately.