Mash together garlic and chiles using a mortar and pestle or the flat side of a large knife. Heat oil in a wok or large skillet over medium-high heat. Add garlic mixture. Cook, stirring constantly, until garlic is just golden, about 20 seconds.
Add chicken; cook, stirring often, until chicken is cooked through, about 4 minutes. Stir in fish sauce, soy sauce, sugar, and 1 1/2 teaspoons pepper. Add basil; cook, stirring constantly, 1 minute. Season with more pepper, if desired. Serve over rice. Garnish with basil.