Heat oil in a large nonstick skillet over high heat. Add chicken, and stir-fry 4 to 5 minutes or just until done. Add carrot, green onions, garlic, and pepper; stir-fry 2 minutes. Add cooked rice; stir-fry 2 minutes or until thoroughly heated. Push rice mixture to sides of pan, forming a well in center. Add egg to center of pan, and cook 30 seconds; toss with rice mixture. Stir-fry until egg is cooked. Stir in soy sauce and water, and cook until thoroughly heated. Sprinkle with cashews.