Heat 1 tablespoon vegetable oil in a large skillet or wok over medium-high heat. Add chicken and stir fry until cooked through. Transfer to a plate.
Heat remaining tablespoon vegetable oil in the skillet, and stir fry shallots, peas, and carrots until tender, about 2 minutes. Add garlic and cook for 30 seconds. Push vegetables to one side of the skillet, and pour the beaten eggs onto the other side to scramble.
Add cooked rice, chicken, soy sauce, and sesame oil, and toss well to combine until the ingredients are heated through.