In a large pot, add the chicken, celery, and onion; cover with water to about 3 inches over the chicken.
Cover the pot, bring to a boil, and then lower the heat to keep a slow simmer going.
Boil the chicken until done, about 1½ hours.
Remove the chicken from the pot and let it cool enough to handle.
Strain the broth and return it to the soup pot; allow the broth to cool enough so that the fat rises to the top and then skim off as much fat as you can.
Turn the heat to about medium and bring the broth to simmering again.
Prepare the carrots and add them to the broth.
Cook them until soft.
In the meantime, remove the chicken from the bones and skin.
Chop or shred the chicken into bite-sized pieces and add the pieces to the soup while the carrots are cooking.
At this point, taste the soup and add salt and pepper and any other spices that sound good to you, such as thyme, summer savory, marjoram, oregano, etc.
(I usually stick to just salt and pepper—we’re purists in our family.
) When the carrots are done, add the cooked noodles and continue to simmer for several minutes to heat thoroughly.