Heat a large heavy bottomed pot that has a lid over MED HIGH heat. Add 1 Tbsp olive oil, then add diced chicken breasts. Sprinkle fajita seasoning mix over chicken and stir. Cook 6-8 minutes, until lightly golden brown and cooked through. Set chicken aside on a plate and cover to keep warm.
To same pot, add remaining 1 Tbsp olive oil and butter. Add onion, and both bell peppers and cook 3-4 minutes, until softened. Add garlic and cook another 30 seconds or so, until fragrant.
Add tomatoes, black beans, chili powder, cumin, paprika, coriander, and chicken broth. Stir together, then stir in rice.
Bring to a boil, then cover, reduce heat to LOW and simmer 20-23 minutes, stirring halfway through. When no excess liquid remains and rice is tender, turn off heat.
Fluff rice with a fork, then stir in 1 cup cheese, cilantro, lime juice, corn, and cooked chicken. Top with remaining 1/2 cup cheese, cover and let sit a few minutes, until cheese is melted.