Whisk together the chicken broth, oyster sauce, fish sauce, soy sauce, white sugar and brown sugar until well blended.
Heat large skillet over high heat. Drizzle in vegetable oil. Add chicken and stir fry until it loses its raw color, 2 to 3 minutes.
Stir in shallots, garlic, and sliced chilies. Continue cooking on high heat about 2 or 3 more minutes.
Add about a tablespoon of the sauce mixture to the skillet; cook and stir until sauce begins to caramelize, about 1 minute.
Pour in the rest of the sauce and add the corn starch.
Cook and stir until the sauce starts to thicken. Continue to cook until sauce glazes onto the meat, 1 or 2 more minutes. Remove from heat.
Stir in basil. Cook and stir until basil is wilted, about 20 seconds. Serve with rice.