Heat 1 teaspoon oil in a large nonstick skillet over medium-high heat. Add celery and snow peas to pan; sauté 3 minutes. Add green peas and water chestnuts; sauté 1 minute.
Push vegetables to one side of pan. Pour egg into other side of pan. Cook, stirring often, until done.
Add cooked rice, tossing well. Stir in remaining sesame oil, soy sauce, and pepper. Cook 1 minute or until rice mixture is thoroughly heated, tossing occasionally. Serve immediately.