In a large pot or Dutch oven, bring the chicken broth to a simmer. Add the chicken breasts and cook for 15-20 minutes, or until cooked through. Remove the chicken to a plate.

Once cool enough to handle, shred the chicken using two forks. Return the shredded chicken to the pot. Bring the broth back to a simmer and stir in the orzo. Cook until al dente, about 8-10 minutes.

While the orzo cooks, whisk the eggs in a medium bowl until pale and frothy, about 2 minutes. Continue whisking while slowly streaming in the fresh lemon juice.

Reduce the soup heat to low. While whisking the egg mixture constantly, slowly ladle about 2 cups of the hot broth into the eggs. Do this one ladleful at a time to prevent scrambling.

Slowly pour the tempered egg mixture back into the pot of soup, stirring constantly. Continue to stir over low heat for 2-3 minutes until the soup has thickened. Do not let the soup boil.

Remove from heat and stir in the fresh dill. Season with salt and pepper to taste. Serve immediately.