In a large pot, place the whole chicken and cover with water.
Bring to a boil over medium heat.
Skim off any foam that rises to the surface.
Add the quartered onion and minced garlic to the pot.
Reduce heat to low and simmer for 30 minutes.
Add the chopped carrots and diced potatoes.
Add the chopped celery and season with salt and pepper.
Continue to simmer until the chicken is cooked through, about 20 minutes.
Remove the chicken from the pot and let it cool slightly.
Shred the chicken meat, discarding the bones, and return the meat to the pot.