In a large skillet or deep sauté pan, heat olive oil over medium heat. Add the diced onion and red bell pepper. Cook for 3–4 minutes until softened. Add garlic and cook another 30 seconds.
Add the chicken pieces and season with salt, pepper, chili powder, cumin, and paprika. Cook for about 5–6 minutes, stirring occasionally, until chicken is mostly cooked through.
Stir in the uncooked rice, black beans, corn, and diced tomatoes (with juice). Pour in the chicken broth and stir to combine.
Bring the mixture to a boil, then reduce heat to low. Cover and simmer for 18–22 minutes, or until the rice is tender and the liquid is absorbed. Stir occasionally to prevent sticking.
Remove from heat and let rest, covered, for 5 minutes. Fluff with a fork, squeeze fresh lime juice over the top, and sprinkle with chopped cilantro. Serve with shredded cheese or sour cream if desired.