Heat the oven to 350 degrees F and grease a 9x13 inch baking dish.
Steam or microwave the broccoli for 2 to 3 minutes, until bright green and just tender, then drain very well.
In a large bowl, stir together the soup, sour cream, broth, garlic powder, onion powder, pepper, and 1 cup of the cheddar until smooth.
Fold in the rice, chicken, and broccoli until evenly coated. Spread into the dish.
Sprinkle with the remaining cheddar and the cracker topping. Cover with foil and bake for 20 minutes, then uncover and bake 10 to 15 minutes more, until bubbling and golden and hot all the way through (165°F / 74°C).
Rest for 5 minutes so the sauce thickens, then serve.