Heat a wok over high heat until smoking. Pour in peanut oil, then immediately add garlic. Stir-fry garlic until it begins to turn golden brown, about 20 seconds. Mix in the ground chicken and continue cooking and stirring until the meat is crumbly and no longer pink, about 2 minutes.
Stir in the sliced chilies, soy sauce, and fish sauce. Cook for about 15 seconds to soften the chilies, then add the basil, and continue cooking until the basil has wilted.