I usually make this in the pressure cooker, to save time. Put the chicken in the pressure cooker, add the water, close the lid and let it boil for 30 minutes. Remove from heat and let it cool down for 10 minutes. Make sure that you follow the safety instructions before you open the lid... You can do it in a regular pot, just cook the chicken for 1 1/2 hour instead of 30 minutes.
Remove the chicken. Add the rice and some salt and bring back to a boil. Let it boil until the rice has "cracked", about 15-20 minutes.
In the meantime prepare the avgolemono. In a big bowl beat the eggs with the lemon juice. Don't add all the lemon at once, begin with one lemon and add the rest in the end, when you taste the soup.
When the eggs and lemon are frothy and the rice is done, then ladle some of the soup in the egg/lemon mix, slowly, while beating. You need to made the egg and lemon mix come to a higher temperature, so that when you add it to the soup the egg won't cook and you won't end up with pieces of egg swimming in your pot. Add at least a cup of the soup in the egg/lemon mix.
Slowly pour the avgolemono in the soup, while stirring the soup. Add some pepper and taste. You can add more salt, lemon and/or pepper until you get the taste you like.
Serve with the chicken on the side. I always put the meat in a plate and sprinkle it with salt, pepper, lemon juice and olive oil. It makes the bland taste of the boiled chicken go away! You can use the leftover chicken to make stir fries, sandwiches, pies, omelettes, pasta etc.
Tip 1: you can save some of the broth (before adding the rice and salt) and put it in the freezer. You have your own homemade chicken broth for risottos etc
Tip 2: The soup should be served hot and freshly made. Otherwise the rice will bloat and you will end up with just tasty rice instead of a soup.
