In a nonstick wok or 12-inch nonstick skillet, heat the oil over high heat.
Add chicken; stir-fry for 2 to 3 minutes or until the chicken is no longer pink in the center.
Add lime peel, gingerroot, garlic, chilies, and cilantro. Stir-fry for 1 minute.
Pour coconut milk over the chicken. Stir in brown sugar, salt, soy sauce, and vegetables.
Reduce heat to medium. Simmer uncovered for 3 to 5 minutes, stirring occasionally until vegetables are crisp-tender.
Spoon into shallow serving bowls; top with basil. Serve with rice if desired.