Place chicken in an 8- to 10-quart pot. Add the water, onions, leek, celery, salt, and pepper. Bring to boiling. Reduce heat; simmer, covered, for 1-1/2 hours or until chicken is almost tender. Add carrots and parsnips; simmer, covered, for 30 minutes more or until chicken and vegetables are tender.
Remove chicken from pot. When cool enough to handle remove and discard skin from chicken. Pull meat from bones, discarding bones. Chop meat, reserving 3 cups (cover and chill or freeze any remaining chopped chicken for another use).
Using a slotted spoon, remove vegetables from broth; set aside. Strain broth through two layers of 100-percent cotton cheesecloth placed in a colander; discard solids. Skim fat from broth. Return broth and vegetables to pot. Add parsley and, if desired, dill weed; heat through. Serve in bowls with Matzo Balls.
In a mixing bowl combine matzo meal, salt, and pepper. Beat in eggs and chicken fat (schmaltz) until well blended. Stir in carbonated water. Cover and chill for at least 2 hours. With wet hands, shape dough into 1-inch balls. Carefully drop dough into a large pot of gently boiling salted water. Cover; simmer for 30 minutes or until Matzo Balls test done (they should be light and cooked all the way through). Do not uncover pot until end of cooking. Remove carefully with a slotted spoon. Serve in hot Chicken Soup. Makes about 30 balls.