Cook the rice according to the package directions.
Heat the oil in a wok or a large nonstick skillet over high heat. Add the carrot, bell pepper, onion, snow peas, mushrooms, chili, and garlic.
Cook, tossing, until the vegetables are just tender, 4 to 7 minutes.
Add the chicken, soy sauce, lime juice, fish sauce, and scallions and cook, tossing, until heated through. Serve with the rice, cilantro, and lime wedges.