In a large saucepan, bring the chicken stock to a boil. Add chicken breasts and simmer 20-25 minutes or until chicken is cooked through and internal temperature registers at least 160°F. Remove the chicken, shred chicken breast, and set aside. Add orzo to the chicken stock and cook 5-8 minutes, until al dente.
In a large bowl, beat egg whites to soft peaks. In a medium bowl, whisk together egg yolks and lemon juice. Fold egg yolk mixture into egg whites. Slowly ladle in some hot stock, whisking constantly. Very slowly, add egg mixture into the pot, whisking constantly. Cook gently until mixture thickens, about 5 minutes. Add shredded chicken and stir. Serve topped with lemon zest and basil.