Heat the vegetable oil in a wok or large skillet over medium-high heat.
Add the minced garlic, sliced shallots, and chopped Thai bird's eye chilies to the pan. Stir-fry for about 1 minute until fragrant and the shallots start to soften.
Add the thinly sliced chicken to the pan and stir-fry for about 3-4 minutes until the chicken is cooked through and no longer pink.
In a small bowl, whisk together the oyster sauce, soy sauce, fish sauce, and sugar until well combined.
Pour the sauce mixture over the cooked chicken in the pan. Stir to coat the chicken evenly with the sauce.
Add the fresh Thai basil leaves to the pan and toss everything together. Continue stir-frying for another 1-2 minutes until the basil leaves wilt.
Remove the pan from heat and serve the Phat kaphrao immediately over steamed jasmine rice. If desired, top with a fried egg.