Trim any fat from the chicken, leaving some skin for richness. Put pieces in the pot with the onion, water to generously cover, salt and pepper. Add the lid, bring to a boil and simmer 30 minutes.
Add the potatoes, rice, Maxima squash cubes and corn with more water to cover and stir to mix everything together. Cover and continue simmering until the chicken, rice and vegetables are nearly tender, 15-20 minutes longer.
Add the green beans and continue simmering until tender, 7-10 minutes. At the end of cooking, the chicken, rice and vegetables should be very tender, almost falling apart. Stir the cilantro into the broth, taste and adjust seasoning. Serve the stew in soup bowls with spoons, knives and forks.
Note: Cazuela can be kept in the refrigerator for 2-3 days and, as you can imagine, it improves each time you reheat it. Add the cilantro just before serving.