Bring the chicken broth to a boil in a saucepan. Stir in the orzo, reduce the heat and simmer, uncovered, for about 10 to 12 minutes, or until pasta is done. Turn off the heat, keeping the pan in its place.
Separate the eggs, and place the egg whites in a clean bowl and beat just until foamy, about 2 to 3 minutes. Add the egg yolks and continue beating until well mixed, another 2 minutes. Continuing to beat, gradually add the lemon juice. Slowly add about 3 cups of the hot chicken broth (at this point, use a thermometer to make sure the broth is just below 160 degrees F), beating as you add the broth in a very thin stream.
Using a wooden spoon or large fork, vigorously stir the orzo and remaining hot broth in an S pattern. Then quickly pour all of the egg lemon mixture into the saucepan while stirring. Keep the pan warm over very low heat, and stir in an S pattern until the soup thickens slightly and the froth is broken down. Serve hot.