Before you start cooking, gently massage the package(s) of rice to break up the grains. If the rice is too firm to loosen in the package, microwave it according to the package directions fur for about half of the time listed on the package. This will soften it just enough to make it easier to separate in the skillet.
Heat 1 tablespoon of oil in a large skillet over MEDIUM-HIGH heat. Add the yellow onion and cook for 1 to 2 minutes, until softened and fragrant.
Add the frozen peas and carrots and stir-fry for 3 to 4 minutes, until fully thawed, heated through, and any excess moisture has cooked off. The carrots should be tender when pierced.
Reduce the heat to MEDIUM and push the vegetables to one side of the pan. Add the remaining 1 tablespoon oil to the empty side, then pour in the eggs and scramble until just set.
Add the rice, break it up with a spoon, and combine it with the other ingredients in the pan. Cook for 3 to 4 minutes, stirring occasionally so it can lightly toast.
Stir in the chicken and cook for 1 to 2 minutes, until warmed through.
Add the soy sauce, sesame oil, and pepper. Stir well to combine and heat through. Taste and adjust seasoning, adding additional soy sauce or a pinch of salt if needed.
Garnish with green onions, if desired, and serve.