Preheat the oven to 350°F (175°C).
In a large bowl, combine the chicken broth, quick-cooking rice, softened cream cheese, chopped green chiles, garlic powder, ground cumin, salt, and black pepper; stir until smooth and evenly mixed.
Spread the rice and chile mixture evenly in a large casserole dish.
Place the trimmed chicken breasts evenly on top of the rice mixture and gently press them into the mixture so they make good contact.
Sprinkle the shredded Monterey Jack cheese over the top of the chicken and rice.
Bake on the middle rack for 40–50 minutes, or until the chicken reaches an internal temperature of 165°F (74°C) and the rice is tender.
Serve hot either with the chicken breasts whole or remove the chicken, shred or chop it, and stir it back into the rice before serving.