Rinse and pat dry the chicken pieces, then chop the carrots, zucchini, corn, and potatoes into bite-sized pieces.
Place the chicken in a large pot and cover it with water or chicken broth. Bring it to a gentle boil over medium heat.
Skim off any foam that forms on the surface to keep the broth clear and clean.
Add chopped onion, minced garlic, and, if desired, a bay leaf or a pinch of oregano. Let it simmer so the flavors combine.
Remove the chicken once it’s cooked through, let it cool slightly, and shred it into smaller pieces.
Add the carrots and potatoes to the simmering broth first. Once they begin to soften, add the zucchini and corn.
Return the shredded chicken to the pot and season with salt and pepper. Stir in chopped cilantro for freshness.
Simmer for a few more minutes, taste for seasoning, and serve hot with lime wedges, warm tortillas, or Mexican rice.