Preheat the oven to 375 degrees.
Grease a 10 inch cast iron skillet well with shortening.
Mix together the cornmeal, water, chicken broth and salt in a medium sized saucepan. Bring to a boil, stirring constantly. Once it reaches a boil, reduce the heat to medium, stirring frequently. Cook for around 6 minutes or until the mixture is very thick.
Remove from heat and let sit for 5 minutes.
Stir the egg into the mixture, making sure it is well blended.
Spread the polenta in a thin and even layer in the bottom of your cast iron skillet.
Bake uncovered for 15 minutes.
Remove from the oven and carefully spread the chili over the polenta. Layer the cheese over the chili and the crushed chips over the top.
Bake again for 20 minutes or until the cheese is melted and the center is set.
Serve with sour cream, fresh chopped cilantro or salsa.