In a large soup pot, heat the olive oil over medium heat. Add the finely chopped onion, sliced carrots, and chopped celery. Sauté until the vegetables are tender and the onion becomes translucent, which should take about 5-7 minutes.

Stir in the minced garlic and cook for an additional minute until it's fragrant. Place the chicken pieces into the pot, ensuring they're nestled among the vegetables.

Pour the chicken broth over the chicken and vegetables. Bring the mixture to a boil, then reduce the heat to low. Cover the pot and let it simmer for about 30 minutes, or until the chicken is fully cooked and tender.

While the soup is simmering, in a separate bowl, whisk together the sour cream, egg yolks, and lemon juice until smooth. This mixture will add a rich and creamy texture to the soup.

To prevent curdling, it's essential to temper the sour cream mixture. Gradually add a ladleful of the hot soup broth to the sour cream mixture, whisking continuously. Repeat this process with a couple more ladlefuls until the mixture is warm.

Slowly pour the tempered sour cream mixture back into the soup pot, stirring constantly to ensure a smooth consistency. Let the soup heat through for an additional 5 minutes, but avoid bringing it to a boil. Season with salt and freshly ground black pepper to taste.

Ladle the creamy chicken soup into bowls, garnish with freshly chopped parsley, and serve immediately.