This soup is to be served in Greek-fashion, at room temperature. Better known as a soup, avgolemono, the Greek mixture of chicken broth, egg yolks and lemon juice, is often used as a sauce.
In a large saucepan, bring the broth to a boil over medium-high heat. Add the rice; reduce heat to medium-low and simmer, covered, 40 minutes.
Combine the eggs, lemon juice, and pepper in a bowl; whisk until frothy. Gradually add 2 cups of the hot broth, whisking constantly to keep the egg mixture from curdling. Pour the egg mixture into the saucepan and cook, stirring constantly, 1 minute longer. Stir in 4 ounces cooked shredded chicken just before serving.