In saucepan, bring chicken stock to boil. Reduce heat and add rice, cover and simmer until tender, about 20 minutes.
In a small bowl, bet eggs and lemon juice. Stirring the egg mixture constantly, add 1 Cup hot soup to egg mixture. (This helps heat up the egg before putting it in the soup. If you don't do this, the heat of the soup will cook the egg and you'd have a cooked egg in the middle of your soup! So, you pour hot soup in your egg mixture slowly..."tempering" the egg.)
Now stir the egg mixture and soup back into the rest of the soup. Simmer until hot but don't boil. Add salt and pepper to taste.