In a medium bowl, whisk together the eggs and 1 teaspoon of the soy sauce. In a large nonstick skillet, heat sesame oil over medium-high. Add egg mixture; stir gently until set. Remove egg; cool slightly. Cut egg into strips; set aside.
In the same skillet, heat canola oil over medium-high. Add carrots, and cook 2 minutes. Add chicken; cook and stir until chicken is no longer pink, about 3 minutes. Then mix in rice and remaining soy sauce; cook and stir for 2 to 4 minutes or until heated through. Add egg mixture and green onion; cook and stir for 2 minutes more.
