In a large pot, combine chicken and chicken broth.
Add diced onion and carrots to the pot.
Let the soup simmer for about 20 minutes, or until the chicken is cooked through.
Remove the chicken and shred it into bite-sized pieces.
Stir in the orzo and simmer for another 8-10 minutes until tender.
Meanwhile, whisk together eggs and lemon juice in a bowl.
Gradually add a ladle of hot broth into the egg-lemon mixture, whisking continuously.
Remove the pot from heat and stir in the egg-lemon mixture slowly.
Return the shredded chicken to the pot and add fresh dill, salt, and pepper.
Serve hot, drizzling extra lemon juice if desired.