In a small stock pot, heat the stock and water to a boil.
Reduce heat and add orzo, simmer for 7 minutes.
Meanwhile, whisk the egg yolks in a medium bowl. Remove a cup of the hot stock and slowly drizzle it into the egg yolks, while whisking. This will stop the eggs from scrambling when they mix with the hot soup.
Reduce heat to medium low, slowly whisk the eggs into the soup in the pot.
Simmer the soup for 3 to 5 minutes, stirring the constantly.
Remove from heat, Stir in chicken, lemon juice, salt and white pepper.