Cover chicken and cook for 20 to 30 minutes or until done. Remove meat from bones. Set aside.In a dutch oven over medium-high heat, saute onions and garlic for 2 minutes. Add chopped green chilies, then rinsed beans. Pour chicken broth into the pan. Add sliced jalapenos. Season with salt, pepper, and cumin. Place lid on pot and reduce heat to low. Cook for 2 hours or until beans are done. Halfway through the cooking process, add 3 cups of cooked chicken.When beans are tender, mix milk with masa (or cornmeal) and pour into the chili. Cook for an additional ten minutes to thicken. Check seasoning and adjust, adding cayenne pepper and paprika if desired.Add some Monterey Jack cheese to the pot and stir to melt. Serve chili in a bowl. Garnish with cilantro, sour cream, extra cheese---even pico de gallo and guacamole, if you have some on hand. Roll up warm corn tortillas and serve on the side of the bowl.