Heat the olive oil in a large skillet over medium heat. Add the chicken pieces and cook until lightly browned on all sides, about 5 minutes.
Add the onion, garlic, and bell pepper to the skillet. Cook until the vegetables soften, about 3 minutes.
Stir in the rice, cumin, chili powder, and salt. Cook for 1 minute so the rice is coated with the spices.
Pour in the chicken broth and the can of diced tomatoes with their liquid. Bring the mixture to a boil, then reduce the heat to low, cover, and simmer for 15 minutes.
Stir in the drained corn. Cover again and cook for 5 more minutes, or until the rice is tender and most of the liquid is absorbed.
Remove the skillet from the heat. Sprinkle the shredded cheese over the top, cover, and let it sit for 2 minutes until the cheese melts.
Serve hot with chopped cilantro and lime wedges on the side.