In a large saucepan, combine chieck broth, bouillon cube, rice, carrots, celery, and onion.

Bring to a boil, then reduce heat.  Cover and simmer for 20 minutes or until rice and vegetables are tender.

Stir in chicken and remove from heat.

Then, in a small saucepan, melt butter and stir in flour until smooth.

Gradually add 2 coups of broth mixture, cook until slightly thickened, stirring constantly.

In a small bowl, beat the eggs until frothy.

Gradually beat lemon juice and 2 cups thickened broth into the large pot of soup.

Very slowly add egg mixture into soup, stirring constantly.  Do not do this if your soup is boiling or very hot or your eggs will split. You may want to take the soup off the burner for a few minutes before you add the eggs.

Heat gently until soup thickens enough to coat a spoon.  Do not boil.

Add salt and pepper to taste, garnish with lemon if you like.