Heat the vegetable oil in a large skillet over medium-high heat. Add the minced garlic and sliced chilies and stir for 30 seconds until fragrant.
Add the sliced chicken to the skillet. Cook for 4 to 5 minutes, stirring often, until the chicken is lightly browned and cooked through.
Stir in the fish sauce, oyster sauce, and soy sauce. Toss everything together so the chicken is evenly coated.
Add the snap peas and cook for another 2 minutes, stirring frequently, until the peas are bright green and still crisp.
Remove the skillet from the heat and fold in the Thai basil leaves until they just wilt.
Divide the cooked jasmine rice among four plates or bowls. Spoon the chicken and snap pea mixture over the rice and serve right away.