Preheat your oven to 375°F and lightly grease a 9x13-inch baking dish.
Heat olive oil in a large skillet over medium heat. Add chicken, season with half the salt and pepper, and cook until no longer pink (about 5-6 minutes). Remove and set aside.
In the same skillet, add chopped onion and garlic. Cook until soft, about 2-3 minutes.
Add uncooked rice and stir for 1 minute. Pour in chicken broth, remaining salt and pepper, and bring to a boil.
Reduce heat, cover, and simmer for 10 minutes. Then stir in broccoli, 1 cup cheddar cheese, sour cream, and cooked chicken.
Transfer mixture to the prepared baking dish. Top with remaining 1/2 cup of cheese.
Cover with foil and bake for 15 minutes. Uncover and bake an additional 10 minutes, or until cheese is bubbly and golden.