In medium bowl, combine fish sauce, soy sauce, and brown sugar, stir in chicken slices to coat. Let marinate 5 minutes.
In nonstick 12-inch skillet, heat vegetable oil over medium-high heat until very hot. Add chicken with marinade and cook, stirring occasionally, until chicken slices lose their pink color throughout, about 3 to 4 minutes. With slotted spoon, remove chicken to plate.
Add onion to marinade remaining in skillet and cook, stirring occasionally, until tender-crisp, about 4 minutes. Stir in chiles, ginger, and garlic, cook 1 minute longer.
4Return chicken to skillet, heat through. Stir in basil leaves just before serving.