Heat the oil in a Dutch oven or soup pan set over medium heat. Add the onion and cook until soft, about 5 minutes.
Add the chicken stock and bring to a boil. Add the rice, reduce the heat, cover the pan, and simmer for 20 minutes or until the rice is tender.
In a mixing bowl whisk the eggs until they are very smooth. Add the lemon juice and whisk. Add 1 cup of the hot broth to the egg mixture and whisk. Set aside.
Add the chicken to the soup, season to taste with salt and pepper and cook for a few minutes to heat up the chicken.
Take the soup off the heat and whisk in the egg-lemon mixture, adding the egg mixture slowly while whisking.
Garnish with fresh parsley and lemon zest if desired.