Heat the vegetable oil in a large skillet or wok over medium-high heat. Add the minced garlic and chopped chilies, stirring for about 30 seconds until fragrant.
Add the chicken pieces to the skillet and cook for 5-7 minutes, stirring occasionally, until the chicken is cooked through and lightly browned.
Stir in the sliced red bell pepper and cook for an additional 2-3 minutes until the pepper is slightly tender.
In a small bowl, mix together the soy sauce, oyster sauce, fish sauce, sugar, and black pepper. Pour this sauce over the chicken and bell pepper, stirring to coat everything evenly.
Add the fresh Thai basil leaves to the skillet and stir until wilted, about 1 minute. Remove from heat.
Serve the Thai basil chicken over cooked jasmine rice.