Prepare the Oven: Preheat the oven to 350°F.
Cook the Rice: Prepare the quick-cooking white rice according to the package directions, yielding about 4 cups of cooked rice.
Sauté the Vegetables: Melt the butter in a large skillet over medium heat. Add the chopped onion and broccoli florets, then cook until the onion becomes transparent. Create the Cheese Sauce: Add the cream of chicken soup, 4 ounces of the cheese, and the milk to the skillet. Stir until the cheese has completely melted and the mixture is smooth. Combine the Rice: Remove the skillet from the heat and stir the cooked rice into the cheesy broccoli mixture until evenly incorporated.
Fill the Casserole Dish: Lightly grease an 8×8-inch casserole dish, then transfer the rice and broccoli mixture into the dish and spread it evenly.
Add the Topping: Shred or crumble the remaining 4 ounces of cheese over the casserole. Sprinkle the crushed potato chips evenly over the cheese. Bake the Casserole: Bake at 350°F for 30 minutes, until the cheese on top is melted, the potato chips are beginning to turn golden brown, and the casserole is bubbly.