In a soup kettle; cover chicken, celery, carrots, onion, bay leaf, peppercorns and salt with cold water. Bring to a boil and immediately reduce to a simmer. Partially cover the pot, allowing steam to escape. Cook for 1 ½ hours, skimming off impurities as they rise to the top. If you place the soup kettle ½ on the heat, it will push the impurities and fat to the side of the kettle that is off the heat. This will make it easier to skim off.
Place the colander over a large bowl. Strain the broth through the colander into the bowl. Set the chicken and vegetables to the side to cool. Strain the broth a second time through a fine sieve. You can also refrigerate the broth overnight and the fat will solidify, making it easy to remove the next day.
Once the chicken and vegetables have cooled. Pull meat from the bones and chop carrots. Discard bones, celery and onions.
Bring the broth to a boil. Reduce heat to medium low. Add the chicken, carrots and rice and cook until rice is cooked through, about 20-25 minutes. Reduce heat to keep warm.
Make the Avgolemono Sauce (with warm broth added).
Slowly add the sauce, gently stirring into the soup. Season with salt and fresh ground pepper. Serve.