Preheat oven to 350 degrees [F].
In a medium mixing bowl, combine eggs, buttermilk, butter, and corn and blend well.
Combine corn meal, baking powder, and salt in a large mixing bowl. Pour liquid gradually, but quickly, into corn meal, mixing just until dry ingredients are moistened; do not overmix. Turn batter into a greased 8-inch square cake pan. Sprinkle chilies and cheese over the top and bake in the center of the oven for 45 minutes, or until top is golden brown.