Heat large skillet over medium-high heat. Drizzle in oil. Add chicken, seasoned with salt and pepper, and stir fry until it loses its raw color, 2 to 3 minutes. Stir in shallots and garlic. Continue cooking on until some of the juices start to caramelize in the bottom of the pan, about 2 or 3 more minutes. Add the sauce mixture to the skillet; cook and stir until sauce begins to caramelize, about 1 minute.