2. Add 2 more teaspoons of oil to the pot. Add onions, celery, carrots and thyme and cook until the vegetables are tender, about 5 minutes. Add 5 cups of the chicken broth and 1 cup of water and bring to a boil. Let simmer about 8 minutes. Turn heat down to low to keep soup hot.
3. Warm remaining 1 cup chicken broth in a small saucepan until it's hot, but not boiling. In a medium bowl, beat eggs and gradually whisk lemon juice into the eggs. Then gradually add the hot broth to the egg-lemon mixture, whisking the entire time. Add the mixture to the soup, stirring well until the soup is thickened. Add cooked chicken back to the soup and season with salt & pepper. Do not let soup come to a boil or it will curdle.
4. Add 1/2 cup rice to bowl and pour soup over the top, enjoy!