Greek Lemon Chicken

1 chicken (3 1/2 to 4 lb.)
1 med onion -- chopped (approximately 1 1/2 cups)
1 med carrot -- chopped (approximately 1/2 cups)
3 rib celery -- chopped (approximately 1 1/2 cups)
8 cup water
2 tsp. salt -- plus to taste
1 cup long grain white rice
4 eggs -- at room temperature
1 teaspoon cornstarch
2 tablespoon cold water
1/4 cup lemon juice -- plus more to taste (approximately 2 lemons)

Instructions
1. Place chicken, chopped vegetables and water in a large 6-8 qt. pot. Bring to a boil, reduce heat to low and simmer for 1 1/2 hours, skimming broth frequently and turning chicken at midway point. Remove chicken from pot and reserve for another use. Strain broth through a fine mesh sieve or cheesecloth, discarding vegetables. You should have about 6 cups of cooking liquid - slightly more is fine, but if you have less, add enough water to bring the amount to 6 cups. Return liquid to pot, add salt and bring to a simmer. Reduce heat to low, add rice and cook until tender, approximately 20 minutes, stirring occasionally. Turn off heat.

2. Place eggs and cornstarch in blender container. Whip on high speed 2-3 minutes until very frothy. Add cold water and lemon juice and whip 20-30 more seconds. Transfer mixture to a large bowl and slowly whisk in 3-4 cups of hot soup. Add tempered egg mixture to remaining soup, stirring constantly so that mixture will not break. Soup should be creamy with a light skim of foam on top. Season to taste with more salt and lemon juice as needed and serve immediately.