Preheat your oven to 425F or heat a gas grill to medium-high. Tear four 12x18 inch sheets of heavy-duty foil and lay them on your counter. If using regular foil, double it up so the packets don't leak.

In a large bowl, toss the chicken strips with 1 tablespoon olive oil and half the fajita seasoning. In a second bowl, toss the peppers and onion with the remaining 2 tablespoons olive oil, lime juice, and the rest of the seasoning. This two-bowl method keeps the chicken from overcooking while the vegetables soften.

Divide the pepper and onion mixture among the four foil sheets, mounding it in the center. Top each with an equal portion of seasoned chicken. Fold the long sides of foil up and over the filling, then fold down twice to seal. Fold in the short ends twice, crimping tightly to trap steam. Leave a little air space inside for heat circulation.

Place packets on a rimmed baking sheet if baking, or directly on the grill grates. Cook for 22 to 25 minutes, until the chicken reaches 165F and the vegetables are tender-crisp. Carefully open one packet away from your face - hot steam will escape. The chicken should be opaque throughout with no pink.

Let packets rest 2 minutes, then open carefully. Squeeze extra lime over the top if you have it, sprinkle with cilantro, and serve directly from the foil or slide onto warm tortillas with sour cream on the side.