Season the Chicken: Place the chicken pieces in a bowl and sprinkle with Tex Mex seasoning, chili powder, and cumin. Toss until every piece looks well coated and ready to cook.
Brown the Chicken: Heat olive oil and butter in a large deep skillet over medium heat. Add the chicken and cook until lightly golden on the outside. Stir gently so it cooks evenly. Remove the chicken and set it aside.
Cook the Vegetables: Add the chopped onion and bell peppers to the same skillet. Stir and cook until softened. Add garlic and cook just until fragrant.
Add Rice and Tomatoes: Stir the rice into the vegetables and let it toast briefly. Pour in the fire roasted tomatoes and chicken broth. Stir well, scraping up any flavorful bits from the bottom.
Simmer Everything Together: Return the chicken to the skillet. Bring the mixture to a gentle simmer, cover, and cook until the rice turns tender and absorbs most of the liquid.
Add Beans and Corn: Stir in the black beans and corn. Cover again and cook a few more minutes until everything heats through and blends nicely.
Melt the Cheese: Sprinkle Monterey Jack cheese over the top. Cover and let it melt into the rice. Remove from heat and let it rest briefly.
Finish and Serve: Top with fresh cilantro and squeeze lime juice over each serving for a bright finish.