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Heat olive oil in a large skillet over medium heat.
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Add onions and sauté until softened.
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Turn up heat to medium-high, salt and pepper chicken, then add chicken to pan.
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Cook chicken until no longer pink inside, then add garlic. Cook for 1 minute.
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Add rice and chicken broth to the pan and bring to a boil. Reduce heat, cover, and let simmer for 12 minutes.
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Stir the broccoli into the rice mixture, cover, and let simmer for another 8 minutes, or until broccoli and rice are both tender.
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Add 1/2 cup cheese to the rice mixture and stir until melted.
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Sprinkle the remaining cheese over the dish and cover for 2-3 minutes, until cheese is fully melted.