Combine 2 2/3 cups water, rice and 1/4 teaspoon of salt in a rice cooker, and cook according to the manufacturer's instructions. Transfer the steamed rice to a baking sheet to cool to room temperature. Cover and refrigerate until cold.
Heat 1 tablespoon of canola oil in a large wok over medium-high heat. Add the eggs and stir with a fork for about 30 seconds or until just cooked. Remove the eggs from the wok and set aside on a plate.
Heat 1 tablespoon of oil in the wok, season chicken with salt and pepper and cook for 4 to 5 minutes or until golden brown and cooked through. Remove chicken to a plate. Heat the remaining 3 tablespoons of canola oil in the wok over medium-high heat.
Add the carrots and broccoli to the wok, and stir-fry for 2 minutes. Add the cold rice, and stir-fry for 2 minutes or until heated through. Season with salt and pepper. Stir in the eggs, chicken and 3/4 of the green onions. Add the soy sauce and sesame oil and continue to stir-fry for 1 minute. Transfer the rice to a bowl and sprinkle with the remaining green onions.