Heat olive oil in a large skillet. Add chopped onion, garlic and cubed chicken. Cook on medium heat for a few minutes until chicken start to brown a bit. Season with salt and pepper to taste.
Add rice, cream of chicken soup and chicken broth. Start with 2 cups of chicken broth and if more is needed until rice is fully cooked, add more. Cook over medium heat until rice is fully cooked, should take about 15 minutes or so. Taste for seasoning and adjust as necessary.
Add half the cheese and the broccoli florets and continue cooking for 2 more minutes, until broccoli softens a bit. Sprinkle over the top with remaining cheese and place skillet under broiler for a couple minutes, just until it melts and starts to brown a bit.