1. Heat oil in large stockpot over medium heat. Add onion, carrots, celery, salt and pepper; sauté 6 to 8 minutes. Stir in broth and chicken, bring to a simmer.
2. Add rice and cook 20 minutes until rice is tender. Remove pot from heat.
3. In a large mixing bowl, whisk eggs and lemon juice. In 1/2 cup increments (about 1 ladle full), transfer 1 1/2 cups hot chicken broth from stockpot to egg mixture, whisking after each addition. The bowl should be slightly warm to the touch.
4. Slowly add egg mixture to stockpot, stirring to thicken.
5. Serve, garnished with parsley.