Put the chicken in a large pot and cover with water. Cook over medium heat, skimming the foam that rises to the surface, until tender, about 1 hour. Transfer the chicken to a plate and season with salt and pepper to taste. Add the rice to the chicken broth and season with salt. Cook until soft, about 15 minutes. Remove from the heat.
Beat the egg whites with an electric mixer until almost stiff peaks form. Add the yolks, one at a time, lightly beating after each addition. Add the lemon juice and beat 1 minute. Remove a cup of the warm broth from rice mixture and slowly beat into the egg mixture until blended. With a wooden spoon, gently stir the egg mixture into soup (do not stir vigorously). There should be a layer of egg foam resting on the top of the soup. Serve the chicken alongside the soup.
Serves 4 to 6