Cut the celery stalks into 1-inch pieces
Quarter the onion
Add the water to a large pot
Place the whole chicken in the pot
Add the half the carrots, half the celery, and pepper to the water
Bring to a boil over high heat
Reduce heat to medium
Simmer for 30 minutes, skimming any foam that rises to the top
Transfer the chicken to a bowl and let it cool, about 20 minutes
Strain the broth, discarding the vegetables
Return the broth to the large pot
Add the remaining carrots and celery to the broth and simmer over medium heat until tender, about 10 minutes.
When the chicken is cool enough to handle, remove the meat from the chicken carcass, discarding the skin & bones
Shred the chicken and add it to the broth
Continue simmering over medium heat for 10 minutes
Ladle into individual bowls
Serve