In a large pot, bring the chicken broth to a boil over medium-high heat.
Add the orzo pasta to the boiling broth and cook according to package instructions, usually about 8-10 minutes, until al dente.
While the orzo is cooking, whisk together the eggs and lemon juice in a medium bowl until well combined.
Once the orzo is cooked, reduce the heat to low. Gradually ladle about 1 cup of the hot broth into the egg and lemon mixture, whisking constantly to temper the eggs.
Slowly pour the tempered egg mixture back into the pot, stirring continuously. This will help prevent the eggs from curdling.
If using, add the shredded chicken to the soup and heat through for about 2-3 minutes.
Season with salt and pepper to taste. Remove from heat and let sit for a few minutes to thicken slightly.
Serve hot, garnished with fresh dill or parsley.