If you don't have a wok, a large nonstick skillet works just as well. Just make sure it's at least 12 inches; stir-fries need space.
In a medium bowl, combine lime juice, cilantro, 1 Tbsp. oil, soy sauce, 1 tsp. garlic, brown sugar, cumin and chili powder. Add chicken; stir well. Let stand for 15 minutes. In a 12-inch nonstick skillet, heat 1 1/2 tsp. oil over medium-high heat until very hot; swirl to coat skillet. Spread half of chicken in a single layer, reserving marinade. Cook, undisturbed, for 2 minutes, then stir-fry for 1 minute. Transfer to a plate. Add another 1 1/2 tsp. oil; repeat with remaining chicken. Add remaining 2 tsp. oil, peppers and onion to skillet. Stir-fry until vegetables are slightly charred and crisp-tender, about 5 minutes. Add remaining 1 Tbsp. garlic; stir-fry for 30 seconds. Season with salt. Pour reserved marinade into skillet; let boil for 30 seconds. Return chicken and any juices that have collected to skillet; toss until heated through. Serve with warm tortillas, if desired.