Stir the oyster sauce, fish sauce, soy sauce, dark soy sauce, sugar, and 1 tablespoon of water together. Set it next to the stove.
Heat 1 tablespoon of oil in a wok or large skillet over high heat until it just starts to smoke. Add the garlic, chilies, and shallot and stir for 30 seconds.
Add the ground chicken and spread it into one layer. Leave it alone for a full minute so it browns, then break it up and stir-fry for 3 to 4 minutes until cooked through.
Pour in the sauce and toss for 30 seconds until everything is glossy. Turn off the heat and fold in the basil. It wilts in seconds.
In a separate small pan, heat the remaining 2 tablespoons of oil over medium-high and fry the eggs until the edges are crispy and the yolks are still runny, about 2 minutes.
Serve the chicken over rice with a fried egg on top. Break the yolk before you eat. That is the sauce.