Heat oven to 375 degrees F. Butter a shallow 2-quart or 9- by 13-inch broiler-proof baking dish.

In a large bowl, whisk together the eggs, sour cream, mayonnaise, soup, and 1/2 teaspoon pepper; stir in the onion and all but 1/4 cup cheese. Fold in the chicken, rice, and then the broccoli.

Transfer the mixture to the prepared dish, cover with nonstick foil and bake for 30 minutes. Remove from the oven and heat the broiler.

In a small bowl, combine the potato chips and the remaining cheese. Sprinkle over the casserole and broil until golden brown, 3 to 4 minutes.