For the chicken soup: Place chicken, celery, carrots, onion, dill, parsley, pepper and salt to taste in a pot and cover with water. Let soup simmer for 1 hour and 15 minutes.
For the matzo balls: Crack the eggs into a large bowl and beat with a fork to mix thoroughly. Beat in the schmaltz, then add the pepper and 1/4 teaspoon salt.
Stir in the matzo meal, then mix vigorously with a wooden spoon until completely blended and very stiff. Let stand for 30 minutes. (It can be refrigerated, covered with plastic wrap, until ready to use, up to 8 hours.)
Fill a large, wide pot three-quarters full with water. Add the remaining tablespoon salt and bring to a boil over high heat.
Wet your hands with cold water so the batter doesn't stick to them. Holding and rolling the mixture between your palms, shape it into perfect balls about 1 1/4 inches in diameter. (They will double in size when cooked.)
Gently place the matzo balls in the boiling water. When all have been added, decrease the heat so the water simmers briskly, but isn't at a rolling boil, when the pot is covered. Cook for 25 minutes.
Cut chicken meat into bite-sized pieces. You can add it to the soup, just before serving, or save it for chicken salad.
Strain the soup, and discard all solids except for the carrot and celery. Add salt and pepper to taste. Slice carrot and celery, then toss into soup. Also add the chicken pieces if desired. Transfer matzo balls to soup with a slotted spoon.
This recipe was provided by a chef, restaurant or culinary professional. It has not been tested for home use.