In a large bowl, whisk together lime juice, 2 tablespoons olive oil, garlic, cumin, smoked paprika, chili powder, oregano, salt, and pepper. Add sliced chicken strips and toss to coat evenly. Let marinate at room temperature for 15 minutes (or refrigerate up to 4 hours for deeper flavor).

Heat a large cast-iron skillet over high heat until smoking hot. Add a drizzle of olive oil, then carefully place the marinated chicken strips in a single layer (work in batches if needed). Sear for 3-4 minutes without moving, until deeply charred. Flip and cook another 2-3 minutes until chicken is cooked through and reaches an internal temperature of 165°F (74°C). Transfer to a plate and keep warm.

In the same skillet, add 1 tablespoon olive oil, then toss in the sliced peppers and onion. Cook over high heat, stirring only occasionally, until softened and lightly blistered, about 5-6 minutes. You want them to retain some crispness and get dark edges.

Return the cooked chicken to the skillet with the vegetables and toss to combine. Remove from heat and squeeze additional lime juice over the fajitas. Sprinkle with chopped fresh cilantro. Serve immediately, still sizzling in the skillet, alongside warm tortillas and your choice of toppings.