In a large pot, add the whole chicken and cover with water.
Bring the water to a boil over medium-high heat.
Skim off any foam that rises to the surface.
Add the quartered onion, minced garlic, and bay leaf to the pot.
Reduce the heat to low and cover, simmering for 30 minutes.
After 30 minutes, add the sliced carrots and chopped celery.
Continue to simmer for an additional 20-30 minutes until the chicken is cooked through.
Remove the chicken from the pot and let it cool slightly.
Shred the chicken into bite-sized pieces, discarding the bones and skin.
Return the shredded chicken to the pot, season with salt and pepper to taste, and serve hot.