Wash the chicken with cold water and place in pot. Cover with water and bring to a simmer (do not boil or your broth won't be clear).Skim off bubbling foam as it forms.
Add celery, carrots, onion, herbs, salt and pepper and continue to simmer for about 45 minutes.
Pour soup through strainer and let cool. When broth has completely cooled, remove the chicken meat and skim off the fat and save for the matzo balls.In a mixing bowl, mix together 4 eggs and 4 tablespoons chicken fat (or vegetable oil). Stir in the matzo meal and salt.
Add 1/4 selter water. Cover and refrigerate for at least 1 hour.Form the matzo dough into teaspoon-size balls.Bring the chicken broth to a boil.
Add the matzo balls, cover, and cook for 20 minutes.