In a large pot, combine the chicken thighs and chicken broth. Bring to a boil over medium-high heat.
Once boiling, reduce the heat to medium-low and let it simmer for about 20-25 minutes, or until the chicken is fully cooked. Remove the chicken thighs and set them aside to cool.
In the same pot with the broth, add the diced onion, garlic, carrots, and celery. Cook for about 5-7 minutes until the vegetables are softened.
Stir in the orzo or rice and cook according to package instructions, usually around 8-10 minutes, until tender.
While the pasta is cooking, shred the cooled chicken into bite-sized pieces.
In a medium bowl, whisk together the eggs, lemon juice, and lemon zest until well combined.
Once the orzo or rice is cooked, ladle a small amount of the hot broth into the egg-lemon mixture, whisking constantly to temper the eggs. Gradually add more broth while whisking.
Pour the tempered egg-lemon mixture back into the pot, stirring gently. Heat the soup for a few more minutes without boiling to thicken slightly.
Add the shredded chicken back into the pot. Season with dried oregano, salt, and pepper to taste.
Remove from heat and garnish with fresh dill or parsley before serving.
Notes
Garnish with fresh dill or parsley for added flavor.