Heat olive oil in a large pot over medium heat. Add diced onion and cook for 5 minutes, stirring occasionally, until softened. Add minced garlic and sauté for 1–2 minutes, until fragrant.
Pour in chicken broth and bring to a boil. Add rice, reduce heat, and simmer for 10–12 minutes, or until rice is tender.
While rice cooks, whisk eggs in a medium bowl until frothy. Slowly add lemon juice, whisking constantly to combine.
Temper the egg-lemon mixture by gradually ladling 1–2 cups of hot broth into it while whisking continuously. Then slowly pour the mixture back into the pot, stirring as you go.
Stir in shredded chicken and heat through for about 5 minutes. Season with salt and pepper to taste.
Ladle soup into bowls, sprinkle with fresh dill, and serve with lemon wedges on the side.