Heat olive oil in a large stockpot over medium-high heat.
Add ground chicken and cook until browned and fully cooked, breaking it into small pieces with a spatula.
Add onion, carrots, and celery to the pot and sauté for 5 to 7 minutes until softened.
Stir in minced garlic and oregano, cooking for 60 seconds until fragrant.
Pour in the chicken broth and bring the mixture to a rolling boil.
Stir in the rice, reduce heat to low, cover, and simmer for 15 to 20 minutes until rice is tender.
In a medium bowl, whisk eggs and lemon juice together until well combined and frothy.
Slowly temper the egg mixture by whisking in two ladles of hot broth from the pot.
Gradually pour the tempered egg mixture into the soup pot while stirring constantly to incorporate.
Heat the soup on low for 2-3 minutes until thickened, ensuring it does not reach a boil, and garnish with fresh dill.