1. Place chicken in crock pot and cover with chicken broth. Cook on high 4 hours, or until chicken is fall off the bone tender.
2. Remove the chicken from the crock pot and allow to cool. Do not discard broth.
3. When the chicken is cool enough to handle, separate bones from meat. Shred meat into small pieces and set aside.
4. Heat olive oil over medium high heat in a dutch oven or large pot. Add chopped onion and saute until softened, about 3-4 minutes. Then add carrots and saute for another 2 minutes.
5. Strain the cooled broth through a mesh sieve. Pour 1 cup into a blender and the rest into the large pot with the onions and carrots. You should have at least 5 cups, add more broth or water if necessary. Heat to low boil and add Orzo, cover and simmer for about 10 minutes.
6. Add lemon juice and eggs to reserved broth in blender and mix until frothy.
7. Slowly pour the egg mixture into the hot soup, stirring constantly until it is mixed in. DO NOT BRING TO A BOIL or eggs will curdle.
8. Add in shredded chicken, dash of white pepper and salt to taste.