In a 5- to 6-quart slow cooker, combine onion, chicken, low-sodium broth, green pepper, jalapeno, 1-1/2 teaspoons of the cumin, 1/4 teaspoon of the cayenne and 1/4 teaspoon of the salt. Cover and cook on HIGH for 4 hours or LOW for 6 hours.
Remove the chicken to a cutting board and allow to cool slightly. Shred the chicken and return it to the slow cooker with remaining 1/4 teaspoon each of the cumin and cayenne, and the tomatoes, corn and beans. Gently mash some of the beans against the side of the bowl to thicken the chili. Stir in the cornmeal and the remaining 1/2 teaspoon salt. Let sit a few minutes to soften the cornmeal. Serve sprinkled with a little of the Monterey Jack cheese.