In a large stockpot over high heat, place the chicken quarters. Cover the chicken with 10 cups of water. Add the ACV, bay leaves, salt, and pepper. Bring this to a boil. Turn the heat to low, cover the pot, and simmer for 1-1/2 hours.

Turn the heat off. Skim any foam from the broth and discard. Remove the chicken and bay leaves from the pot with a slotted spoon to a large bowl. Discard the bay leaves. Set the chicken aside to come to room temperature. Optional: strain the broth through a cheesecloth-lined colander into a large bowl to remove any sediment, foam, and excess fat and return the broth to the pot.

Prepare the vegetables and add the celery, onion, garlic, carrots, and corn to the pot. Turn the heat back to high. As soon as the broth returns to a boil, reduce the heat to low. Cover the pot and allow the soup to simmer for 15 minutes.

Add the zucchini and lemon juice to the soup, cover the pot, and continue to simmer until the zucchini is cooked, approximately 15 minutes longer.

While the soup is finishing cooking, place the chicken on a clean cutting board. Using clean or gloved hands, remove the skin from the chicken and discard it. Take the meat off of the bones and discard the bones. Using 2 forks, shred the chicken. It should pull apart easily.

Add the pulled chicken to the soup, along with the cilantro. Season with salt and pepper to taste. Stir well to combine.

Ladle the hot soup into individual serving bowls and garnish with jalapeño pepper slices, if desired.