Start by heating your cast-iron skillet over high heat until shimmering hot, and add a tablespoon of oil, swirling to coat the surface.
Add the sliced chicken strips to the hot skillet in a single layer. Sear for 3-4 minutes without moving, until edges are golden and crispy, then flip and cook another 2-3 minutes until cooked through. Remove the chicken and set aside.
In the same skillet, add the sliced bell peppers and onions. Cook over high heat, stirring frequently, for about 5-7 minutes. You'll see the peppers blister and char at the edges, and the onions caramelize into a golden, sticky texture with a savory aroma.
Once the vegetables are nicely charred and softened, return the cooked chicken to the skillet. Toss everything together and cook for another 2 minutes to meld the flavors, allowing the smoky edges to cling to the chicken and veggies.
Squeeze fresh lime juice over the skillet contents, giving it a quick stir. The bright citrus will balance the smoky, caramelized flavors. Taste and adjust seasoning if needed.
Garnish with freshly chopped cilantro if desired, and serve hot straight from the skillet with warm tortillas or your favorite sides.