Coat a skillet with cooking spray and place over medium heat; cook and stir eggs until scrambled and set, about 5 minutes. Divide rice between 2 bowls and add eggs to rice.
Grind Thai chile peppers and garlic together with a mortar and pestle or in a food processor.
Coat skillet with cooking spray and heat over medium-high heat; cook and stir pepper-garlic mixture until fragrant and garlic is golden brown, about 1 minute. Add chicken; cook and stir until chicken is about halfway-cooked, about 3 minutes.
Mix soy sauce, oyster sauce, and sugar into chicken; cook and stir until chicken is no longer pink in the center, about 3 minutes more. Add basil and stir for 10 seconds. Remove skillet from heat and continue stirring mixture until basil is wilted; spoon over rice and egg.