First, season the chicken breasts with a pinch of salt and pepper. In a large pot, heat the olive oil over medium heat. Add the chicken breasts and cook for about 6-8 minutes on each side, or until they are fully cooked through. Remove the chicken from the pot and set it aside to cool. Once cooled, shred the chicken into bite-sized pieces.

In the same pot, add the chopped onion and minced garlic. Sauté until the onions become translucent and fragrant, about 5 minutes. Make sure to stir occasionally to prevent burning.

Add the chicken broth and water to the pot, bringing it to a boil. Once boiling, add the orzo pasta. Cook for about 8-10 minutes, or until the orzo is tender.

Reduce the heat to a simmer and return the shredded chicken to the pot. Stir to combine and let it simmer for an additional 10 minutes, allowing the flavors to meld together.

In a medium bowl, whisk together the lemon juice and eggs until smooth. Gradually add a ladle of hot soup to the lemon-egg mixture while whisking continuously. This process, called tempering, prevents the eggs from curdling.

Slowly pour the tempered lemon-egg mixture back into the pot, stirring constantly. Let the soup simmer for another 5 minutes, but do not let it boil. Season with salt and pepper to taste. Ladle the soup into bowls and garnish with fresh dill or parsley.