In a medium bowl, toss chicken with soy sauce and sesame oil. Cover and marinate at room temperature for 10 minutes.

Heat a large nonstick skillet over medium-high heat. Add chicken and marinade and stir-fry until chicken is cooked through, 3 to 4 minutes. Transfer chicken to a plate; set aside. Add vegetable oil to skillet and heat over medium heat. Add onion and cook for 3 minutes. Stir in vegetables and cook for 1 minute. Increase heat to medium-high, stir in rice until incorporated and cooked through, 3 minutes.

Using a wooden spoon, form a well in mixture. Add eggs and scramble within well just until soft. Then break apart and mix into rice; season with salt and pepper. Let cook undisturbed until a golden crust forms, about 1 minute. Turn rice with a spatula and cook other side. Repeat 2 or 3 times until rice is uniformly golden. Add chicken and stir to combine. Serve warm.