Preheat the oven to 400°F (200°C) or prepare a grill. Cut four large sheets of heavy-duty aluminum foil.
In a small bowl, whisk together olive oil, lime juice, cumin, smoked paprika, garlic powder, onion powder, chili powder, salt, and pepper to make a bright marinade.
Place each chicken breast on a foil sheet. Spoon a tablespoon or two of the marinade over each piece, then fold the edges to create a sealed packet. Massage the marinade into the chicken so every side gets a hint of the spices.
Divide the sliced peppers, corn, black beans, and red onion evenly among the four packets, placing them around and on top of the chicken.
Spoon a little more marinade over the vegetables, then seal the packets tightly to trap steam inside.
If using cheese, sprinkle a little at the top of each packet. The cheese melts into a creamy finish as the packets bake.
Bake on a baking sheet for 20–25 minutes, or until the chicken reaches an internal temperature of 165°F (74°C) and the vegetables are tender. If grilling, place packets on indirect heat and cook for about 18–22 minutes, flipping once.
Carefully open a packet to release steam, then squeeze a touch more lime and sprinkle chopped cilantro over the top for a fresh finish.
Serve directly from the foil packets with warm tortillas on the side if you like, letting everyone assemble their own Santa Fe-style wraps.