Place the broccoli into a steamer and steam for 5 to 7 minutes, until it turns bright green.
In a medium saucepan, melt the butter. Add the chopped onion and sauté until the onion becomes translucent.
Add the cheese, cream of chicken soup, broccoli, and rice and stir until the cheese is melted and the mixture is heated through.
You can serve this dish now, or you can put it in an 8-inch square baking pan, cover, and refrigerate. When you are ready to serve, uncover and reheat in a 350°F oven for about 20 minutes, until hot and bubbly.