Pound the garlic and chiles into a coarse paste with a mortar and pestle (or finely mince with a knife). Stir the fish sauce, oyster sauce, soy sauce, and sugar together in a small bowl.
Heat the oil in a wok or large skillet over high heat until shimmering. Add the garlic-chili paste and stir-fry about 30 seconds, until fragrant but not browned.
Add the ground chicken and cook, breaking it into small pieces with a spatula, until no longer pink. Do not crowd the pan or stir constantly — let the meat brown a little.
Pour in the sauce mixture and stir-fry 2 minutes, until the sauce has mostly cooked down and coats the chicken. This dish should not be soupy; the meat absorbs most of the sauce.
Turn off the heat, add the Thai basil, and toss until just wilted — seconds, using residual heat.
Serve over cooked jasmine rice. A fried egg on top is the standard accompaniment in Thailand.