Caldo de Pollo, or Mexican Chicken Soup

lbs chicken

celery sticks, chopped (divided)

onion, diced (divided)

garlic cloves, finely minced (divided)

carrots, chopped

Mexican squash, or zucchini, chopped

jalapeño, finely diced

ears of corn, chopped into 3-inch pieces

water

Salt and pepper

bay leaves

Juice of 2 limes

cilantro, chopped