How to Make It
Preheat the oven to 350°. In a large skillet, heat the oil. Add the onion, garlic, jalapeño and corn kernels and cook over moderate heat until lightly browned, about 6 minutes. Stir in the chile powder and cumin, season with salt and cook for 1 minute. Stir in the tomato paste. Add the chicken and broth and bring to a boil. Simmer over moderate heat until the chili thickens slightly, about 5 minutes. Stir in the cilantro. Pour the chili into a 9-by-13-inch ceramic baking dish.
In a large bowl, whisk the cornmeal with the flour, sugar, baking powder and salt. Stir in three fourths of the cheddar. In a small bowl, combine the milk with the oil and eggs. Add the liquid ingredients to the dry ingredients and stir until evenly moistened.
Spoon the batter over the chili and sprinkle with the remaining cheddar. Bake in the center of the oven for 45 minutes, until the cornbread is golden. Let rest for 10 minutes before serving.