In a large pot, heat the olive oil over medium heat. Add the chopped onion and sauté until it becomes translucent, about 4-5 minutes.
Stir in the minced garlic, diced carrots, and celery. Cook for another 3-4 minutes until the vegetables start to soften.
Add the chicken breasts to the pot and pour in the chicken broth. Bring the mixture to a gentle boil.
Reduce the heat to low and simmer for about 20 minutes, or until the chicken is fully cooked and tender.
Remove the chicken from the pot and set it aside on a cutting board.
Stir in the uncooked orzo pasta into the soup and continue to simmer for an additional 10 minutes, or until the pasta is al dente.
While the pasta is cooking, shred the cooked chicken into bite-sized pieces.
In a separate bowl, whisk together the eggs and lemon juice until well combined.
Once the orzo is cooked, slowly ladle about two cups of the hot soup into the egg mixture to temper it (this prevents the eggs from curdling). Stir continuously while pouring the soup.
Pour the tempered egg mixture back into the pot, stirring continuously to ensure a smooth texture. Add the shredded chicken back into the soup.
Season with salt, pepper, and fresh dill to taste. Heat through, but do not boil.