In a large pot bring sauté the celery, carrots and onion with oil until tender. Add stock and bring to a boil. Add the rice or orzo and continue boiling until it is fully cooked. Stir in the cooked chicken and turn heat down to a low simmer.
In a small bowl combine cornstarch and water, set aside.
In a large bowl, beat eggs with mixer on high for one minute. Beat in cornstarch mixture and lemon juice.
Turn mixer down to medium and VERY VERY slowly drizzle in 1 cup of the hot stock (a tablespoon at a time), while constantly mixing. This will temper the eggs, and prevent them from turning to scrambled eggs. Once the first cup has been added, add in another cup of the hot broth (but can be added in a bit faster, drizzling in about 1/4 cup at a time). Now pour the entire mixture slowly back into the large pot on the stove, about 1/4 cup at a time, while whisking constantly.
Once soup has heated to desired temperature, season with salt and pepper and serve. Keep stove heat on low-medium, do not let it come to a boil or the eggs may still curdle.