Heat the olive oil in a large skillet over medium heat. Add the chicken pieces and cook until they are no longer pink on the outside, about 5 minutes.
Add the diced onion and minced garlic to the skillet. Cook for 2 minutes until the onion softens.
Stir in the uncooked rice, chicken broth, salt, and black pepper. Bring the mixture to a boil, then reduce the heat to low, cover the skillet, and simmer for 15 minutes.
Add the broccoli florets on top of the rice mixture. Cover again and cook for 5 more minutes until the broccoli is tender and the rice has absorbed most of the liquid.
Remove the skillet from the heat. Sprinkle the shredded cheddar cheese over the top and stir gently until the cheese melts and coats the rice, chicken, and broccoli evenly.