Heat the oil in a wok or heavy, high-walled skillet over high heat. As the wok is heating up, whisk together the oyster sauce, soy sauce, fish sauce, and sugar until well-combined. Set aside.
Add the bell pepper and green beans to the hot wok. Stir-fry for one minute. Add in the chicken and stir-fry, breaking apart as you go, until beginning to brown, about 2 minutes.
Stir in the shallots, garlic, and Thai chilies. Cook until fragrant, about 1 more minute. Then, pour in the prepared sauce. Continue to cook until the sauce begins to glaze onto the meat, about 1-2 more minutes.
Stir in the Thai basil leaves and cook until the chicken is completely cooked through, the basil is wilted, and the liquid has mostly evaporated. Serve warm with rice.