Preheat the oven to 350. Separate whites from yolks. Whip whites until stiff. Beat yolks until smooth. Fold yolks into whites and season with salt and pepper. Pour 1/2 of the egg mixture into a greased 9x13. Cut green chilis in half and place half of them face down on top of eggs, then top with half of the cheese. Continue to layer with rest of the egg mixture, chilis, and cheese. Bake for 25 minutes, or until brown.