Heat the olive oil in a large pot over medium heat. Add the onion, carrots, and celery, and cook for 6–7 minutes until softened. Stir in the garlic and cook for 30 seconds more
Pour in the chicken broth, bring to a boil, then add the rice. Reduce to a simmer and cook for 15–18 minutes, until the rice is tender.
Stir in the shredded chicken and let it warm through for 2–3 minutes. Reduce the heat to low.
In a separate bowl, whisk the eggs until frothy, then whisk in the lemon juice.
Ladle about 1 cup of the hot broth into the egg-lemon mixture in a slow, steady stream while whisking constantly. Repeat with a second cup of broth, still whisking.
Remove the pot from the heat. Slowly pour the tempered egg-lemon mixture into the pot while stirring gently. Return to low heat for 1–2 minutes, stirring, until the soup thickens slightly and turns pale yellow. Do not let it boil once the eggs are in.
Season with salt and pepper. Ladle into bowls and top with fresh dill.
