Begin by preparing all ingredients: cut the chicken into strips, mince the garlic, slice the chilies and red bell pepper, and trim the green beans. Set aside.
Heat the vegetable oil in a wok or large frying pan over medium-high heat until hot.
Add the minced garlic and sliced chilies to the oil. Stir-fry for about 30 seconds until fragrant but not burnt.
Add the chicken strips to the wok, and stir-fry until they are no longer pink and are cooked through, about 5-6 minutes.
Toss in the red bell pepper and green beans, stirring continuously for an additional 2-3 minutes until the vegetables are crisp-tender.
In a small bowl, mix together the soy sauce, oyster sauce, fish sauce, and sugar. Pour this sauce over the chicken and vegetables, stirring to coat evenly. Cook for another 1-2 minutes to heat through.
Remove the wok from heat and fold in the Thai basil leaves until they are wilted.
Serve the Thai basil chicken stir fry hot over cooked jasmine rice.