To make the soup on the stove top, combine chicken, onions, celery, carrots, dill, parsley,bay leaf, and 3 quarts water in a large pot (at least 6 qt). Bring the water to a boil, reduce the heat, and simmer, partially covered, for at least five hours. Skim the surface of the soup occasionally to remove any foam that develops.
To make the soup in a pressure cooker, add chicken, onions, celery, carrots, dill,parsley, bay leaf, and water to the pressure cooker as directed in step 1, seal the pressure cooker, and bring it up to full pressure. Reduce the heat,maintaining full pressure, and cook for 30 minutes. Allow the pressure to drop naturally.
Remove the chicken and vegetables from the broth; discard vegetables. Strain the broth, cool, and refrigerate overnight.
When chicken is cool enough to handle, remove the chicken meat from the bones, and chop or shred the meat; cover and refrigerate.
After chilling overnight, skim the fat off the chilled chicken broth and place broth in a pot over medium heat. Add salt and pepper to taste and the reserved cooked chicken, if desired.
