Poach: In a large pot, combine chicken, broth, and bay leaf. Bring to a gentle simmer and cook 15 to 18 minutes, until chicken is cooked through. Remove chicken, shred, and set aside. Discard bay leaf.
Cook rice: Add rice to the simmering broth. Cook 12 to 14 minutes, until tender.
Temper: In a bowl, whisk eggs and lemon juice until frothy. Slowly ladle in 2 cups of hot broth, whisking constantly.
Combine: Remove pot from heat. Slowly stir the egg-lemon mixture into the soup.
Finish: Return shredded chicken to the pot. Stir in olive oil, salt, and pepper. Warm gently over low heat (do not boil) for 2 to 3 minutes.
Serve: Ladle into bowls. Top with fresh dill and serve with lemon wedges.