Season the chicken thighs with salt and pepper. Heat the olive oil in a large pot over medium-high heat. Sear the chicken thighs for 2-3 minutes on each side, then remove and set aside.
In the same pot, add the onion, season with salt and pepper, and cook for 2-3 minutes.
Add the celery, garlic, and oregano. Rub the oregano stems between your hands to release the leaves while keeping the stems intact. Cook for another 2-3 minutes.
Pour in the chicken broth and return the chicken thighs to the pot. Bring to a boil, then reduce the heat, cover, and let it simmer for 15-20 minutes.
Remove the chicken from the pot, shred it, and set aside.
Add the orzo to the pot, increase the heat, and cook for 8 minutes (or cook the orzo separately and add just before serving).
Meanwhile, in a bowl, whisk together the eggs, lemon juice, and lemon zest. Gradually add about 1 cup of the hot broth to temper the egg mixture.
Slowly pour the tempered egg mixture back into the soup, stirring constantly. Let it simmer on low heat for 1-2 minutes. Add the shredded chicken back to the pot.
Serve with fresh dill, bread, and a drizzle of olive oil.
