In a large pot, heat 1 tablespoon of olive oil over medium heat. Add the chicken breasts and cook until browned on both sides (about 5 minutes per side). Remove from pot and set aside.
In the same pot, add the chopped onion, carrots, and celery. Sauté for about 5 minutes until the vegetables are softened. Add the minced garlic and sauté for an additional minute until fragrant.
Pour in the chicken broth and bring to a boil. Once boiling, reduce heat, add the chicken back into the pot, and let it simmer for 15-20 minutes, until the chicken is cooked through.
Remove the chicken from the pot and set aside to cool slightly. Stir the orzo pasta into the broth and cook according to package instructions, usually about 8-10 minutes.
While the orzo is cooking, in a mixing bowl, whisk together the eggs, lemon juice, and lemon zest until well combined.
Gradually ladle about 1 cup of the hot broth into the egg mixture, whisking continuously to temper the eggs. This step is crucial to prevent the eggs from scrambling in the soup.
Slowly pour the tempered egg mixture back into the soup, stirring constantly. Shred the cooked chicken and add it back into the pot. Season with salt and pepper to taste.
Allow the soup to simmer for an additional 2-3 minutes until warmed through and slightly thickened. Remove from heat.
Notes
Garnish with fresh dill and serve with crusty bread.