In a large bowl, toss the cubed chicken with 2 teaspoons of the taco seasoning and the 1/2 teaspoon salt until evenly coated.
Heat the olive oil in a large pot or Dutch oven over medium heat. Add the diced onion and minced garlic and cook, stirring, until the onion softens, about 2 minutes.
Add the seasoned chicken to the pot and cook, stirring occasionally, until the pieces are mostly cooked through and beginning to brown, about 6–8 minutes.
Stir in the chicken broth, diced tomatoes with green chiles, the remaining 4 teaspoons taco seasoning, and the tomato paste until dissolved and combined.
Add the rice, corn, drained black beans, and chopped red bell pepper. Stir to combine, then bring the mixture to a boil over high heat.
Cover the pot, reduce heat to medium-low to maintain a gentle simmer (edges bubbling but not the center), and cook for 20 minutes.
Stir the rice mixture, cover again, and cook on medium for 3–4 more minutes or until most of the liquid is absorbed and the rice is tender.
Squeeze the juice of the lime over the dish and stir. Taste and adjust salt if needed.
Sprinkle the shredded cheddar over the top, cover, and let sit 1–2 minutes until the cheese melts. Serve warm.