In a large stock pot, add 8 cups of water, chicken, 2 celery sticks, ½ onion, 2 garlic cloves, salt, pepper.
Cover and bring to a boil.
Reduce heat and let simmer for 1 hour.
Skim the fat off the top of the liquid.
Reserve the liquid.
Discard the other ingredients from the pot except for the chicken.
Set the chicken aside and let it cool.
Once the chicken is cool enough to handle, remove meat from the bones.
In the same pot, add the remaining celery, onion, garlic, carrots, squash, jalapeño, corn, reserved liquid from the cooked chicken, salt and pepper, bay leaves, lime juice, and chicken.
Make sure the liquid is 2 inches above everything in the pot.
If not, add water and more salt.
Cover and cook for 45 minutes on low heat.
Serve and top with cilantro.