Preheat your oven to 425°F (220°C). In a small bowl, mix all the fajita seasoning ingredients (chili powder through black pepper). In a large mixing bowl, combine the chicken strips, 2 tablespoons of olive oil, lime juice, and the prepared seasoning mix. Toss thoroughly until the chicken is evenly coated.
On a large, rimmed sheet pan, combine the sliced bell peppers and red onion. Drizzle with the remaining 1 tablespoon of olive oil and toss to coat. Spread the vegetables into a single, even layer.
Nestle the seasoned chicken strips evenly among the vegetables on the sheet pan, ensuring they are in a single layer and not overlapping.
Place the sheet pan in the preheated oven and bake for 25-30 minutes, or until the chicken is cooked through (internal temperature of 165°F / 74°C) and the vegetables are tender and slightly charred at the edges.
Remove the pan from the oven. Immediately sprinkle the chopped cilantro over the hot chicken and vegetables. Serve directly from the sheet pan, with lime wedges for squeezing and warm tortillas on the side for assembling fajitas.