Preheat the oven to 350 degrees.
Cut chicken into bite-sized pieces and season with salt, pepper, garlic powder, and onion powder.
Heat butter in a large pot over medium heat until melted. Add the chicken and cook until golden brown on all sides, about 5 minutes. Remove and set aside. Note: This step is not needed if using a cooked rotisserie chicken.
Add the chicken broth, olive oil, and rice to the pot and bring to a boil, then reduce heat to a simmer.
Cover tightly and cook for 7 minutes.
Add the broccoli to the rice and turn off the heat. Cover and let stand for 10 minutes, do not stir.
Add the cooked chicken, soup, milk, sour cream, and half of the cheddar cheese. Stir only to combine.
Add to a lightly greased 9 x 13 casserole dish and top with remaining cheese.
Cover and bake for 15 minutes.
Melt the butter and crumble up the crackers. Combine to form the topping for the casserole.
Top the casserole with the crumbled cracker topping and bake uncovered for 10 additional minutes.
Let the casserole sit for 5 minutes prior to serving.