Heat olive oil in a large pot over medium heat. Add the diced onion and cook for about 5 minutes, stirring occasionally, until softened. Add the minced garlic and sauté for another 1-2 minutes, just until fragrant.

Pour in the chicken broth and bring it to a boil. Add the rice and reduce to a simmer. Cook for 10-12 minutes, or until the rice is tender.

While the rice cooks, whisk the eggs in a medium bowl until frothy. Slowly add the lemon juice, whisking constantly to combine.

Gradually ladle 1-2 cups of hot broth into the egg-lemon mixture, whisking continuously. Once tempered, slowly pour the mixture back into the pot, stirring as you go.

Stir in the shredded chicken and let it heat through, about 5 minutes. Be careful not to boil the soup after adding the egg mixture. Season with salt and pepper to taste.

Ladle the soup into bowls, top with a sprinkle of fresh dill, and serve with lemon wedges on the side.