In a large skillet with a lid, heat olive oil over medium heat.
Add the chopped onion and cook for 3–4 minutes, stirring occasionally, until softened and translucent.
Meanwhile, in a medium bowl, toss the chicken with the taco seasoning until evenly coated.
Add the seasoned chicken to the skillet and cook, stirring occasionally, until no longer pink on the outside and lightly browned, about 4–5 minutes. (The chicken will finish cooking later.)
Stir in the minced garlic and cook for 1 more minute.
Add the diced tomatoes with green chilies (with their juices), tomato sauce, chicken broth, black beans, and rinsed rice. Stir until well combined.
Bring to a gentle boil, then reduce the heat to medium-low. Cover and simmer for 18–22 minutes, stirring once halfway through, until the rice is tender and most of the liquid is absorbed.
Remove the lid, stir gently, and sprinkle the shredded Monterey Jack cheese evenly over the top. Cover for 2–3 minutes to melt the cheese. Or, place the skillet under the broiler for 1–2 minutes until the cheese is bubbly and lightly golden (watch carefully).
Remove from heat. Garnish with tomatoes and chopped fresh cilantro.
Serve warm, topped with sour cream and a squeeze of lime, if desired.