Trim off neck flap all the way up to the top of the chicken's wishbone. Trim fat and skin from around the back cavity of the chicken. Reserve both. Cut chicken into quarters. Place chicken in large pot with onions and cover with about 4 litres water. Bring to the boil, reduce heat and simmer 2 hours.
Add carrots and celery to the pot; simmer an additional hour. Season to taste with salt.
Remove chicken pieces and set aside. You may reserve them for another use or shred the meat for the soup. Keep the chicken covered at room temperature before shredding.
Dice reserved skin and fat into 2.5cm pieces. Cook in a heavy bottomed frying pan over medium heat, turning occasionally. Make sure the pan never gets so hot as to cause the rendered fat to smoke. When the skin is crisp and brown, remove to a cutting board and drain the fat (schmaltz) into a small non-plastic bowl to cool slightly. When cool enough to handle, mince the skin finely.
To make the matzoh balls, blend schmaltz or oil and eggs together. Mix together matzo meal and salt. Combine the two mixtures and mix well. Add 4 tablespoons stock or water; mix until uniform. Stir in minced skin. Cover bowl and place in refrigerator for 20 minutes.
Bring soup to the boil. Meanwhile, roll matzoh mixture into 2.5cm balls. Reduce heat and drop balls into soup. Add dill. Cover pot, and cook 30 to 40 minutes. DO NOT REMOVE THE COVER FROM THE POT WHILE COOKING!
Schmaltz is used often in Jewish cuisine and is rendered chicken or goose fat. If you don't want to use the schmaltz to make the matzoh balls, simply use vegetable oil.