In a large pot, heat the olive oil over medium heat. Add the diced onion and sauté until translucent, about 5 minutes.
Stir in the minced garlic, sliced carrots, and celery, and cook for another 3-4 minutes until the vegetables are slightly softened.
Pour in the chicken broth and bring to a boil. Add the chicken breasts and orzo pasta to the pot. Reduce heat to medium-low and simmer for about 15-20 minutes, or until the chicken is cooked through and orzo is tender.
Once the chicken is cooked, remove it from the pot and shred it with two forks. Return the shredded chicken to the pot.
In a small bowl, whisk together the eggs, lemon juice, and lemon zest until well combined. Temper the egg mixture by slowly adding a ladle of the hot soup into the bowl while whisking continuously.
Gradually add the tempered egg mixture back into the soup, stirring gently to combine. Avoid bringing the soup back to a boil to prevent curdling.
Season the soup with dried oregano, salt, and pepper to taste. Remove from heat.
Garnish with fresh dill or parsley before serving.
Notes
For a gluten-free option, substitute orzo with rice.