In a large skillet, heat the olive oil over medium heat. Add the diced chicken and season with salt and pepper. Cook until browned and cooked through, about 5-7 minutes. Remove the chicken from the skillet and set aside.
In the same skillet, add the chopped onion and bell pepper. Sauté for about 3-4 minutes until softened. Add the minced garlic and cook for an additional 1 minute until fragrant.
Stir in the uncooked rice, black beans, diced tomatoes (with juices), chicken broth, taco seasoning, and cumin. Bring the mixture to a boil.
Reduce the heat to low, cover the skillet, and simmer for 18-20 minutes, or until the rice is tender and has absorbed most of the liquid.
Return the cooked chicken to the skillet, stirring to combine. Sprinkle the shredded cheddar cheese on top, cover, and let it sit for 2-3 minutes until the cheese is melted.
Serve the skillet hot, topped with diced avocado, fresh cilantro, and lime wedges on the side.