Heat the vegetable oil in a large skillet or wok over medium-high heat.
Add the minced garlic and chopped chilies to the skillet, stirring for about 30 seconds until fragrant.
Increase the heat to high and add the ground chicken. Cook, breaking it apart with a spatula, until browned and cooked through, about 5-7 minutes.
Stir in the soy sauce, oyster sauce, fish sauce, and sugar. Mix well and cook for an additional 2 minutes.
Remove the skillet from heat and fold in the fresh Thai basil leaves until just wilted.
Serve the Thai basil chicken over cooked jasmine rice, garnished with sliced cucumber and lime wedges.