Step 1: In a medium bowl, combine the thinly sliced chicken, 1 tablespoon of olive oil, 1 tablespoon of lime juice, and 2 tablespoons of fajita seasoning. Toss to coat evenly. Let marinate at room temperature for at least 20 minutes, or refrigerate for up to 2 hours.
Step 2: Heat 1 tablespoon of olive oil in a large cast-iron skillet or heavy-bottomed pan over medium-high heat until shimmering. Add half of the marinated chicken strips in a single layer (do not overcrowd). Cook for 2-3 minutes until browned, then stir and cook for another 2-3 minutes until cooked through. Remove chicken to a plate and set aside. Repeat with remaining chicken if necessary.
Step 3: Add the sliced bell peppers and onions to the same skillet. Sauté for 5-7 minutes, stirring occasionally, until the vegetables are tender-crisp and slightly charred. Sprinkle with any remaining fajita seasoning if desired.
Step 4: Return the cooked chicken to the skillet with the vegetables. Toss everything together to combine and heat through, about 1-2 minutes. A final squeeze of fresh lime juice can be added for brightness.
Step 5: While the fajita mixture is heating, warm your tortillas. Serve the sizzling chicken and vegetable mixture immediately with warm tortillas and your favorite toppings.