Preheat the oven to 400°F (200°C) and lightly grease a 9×13-inch baking dish.
Pat the chicken dry with paper towels and cut it into evenly sized bite-sized pieces.
Place the chicken in a large bowl and add smoked paprika, chili powder, cumin, garlic powder, onion powder, oregano, black pepper, salt, cayenne, olive oil, and lime juice.
Toss until the chicken is evenly coated with the seasoning mixture.
Slice the bell peppers and onion into thin but substantial strips and gently toss them with the seasoned chicken.
Stir the Greek yogurt with a small pinch of the fajita seasoning in a separate bowl.
Spread the chicken and vegetables evenly in the prepared baking dish, keeping the pieces in as close to a single layer as possible.
Spoon small dollops of the seasoned Greek yogurt over the chicken and vegetables.
Bake for approximately 18–22 minutes, or until the chicken reaches an internal temperature of 165°F (74°C).
Carefully remove the baking dish from the oven and sprinkle the shredded cheese evenly over the top.
Return the dish to the oven for 3–5 minutes, until the cheese is melted and bubbly. Broil for 1–2 minutes if you want a more golden top, watching carefully.
Let the chicken rest for about 5 minutes before serving.
Finish with fresh cilantro and an additional squeeze of lime if desired.