Sprinkle cumin over the chicken and rub in. Put chicken and lime juice to a container with a tight lid, cover and shake to mix well. Marinate in the refrigerator, 2 to 24 hours, shaking the container occasionally. About an hour before cooking the chicken, remove it from the marinade, pat dry with paper towels and set aside to allow it to come to room temperature.
Add half of the oil to a medium, nonstick skillet over medium high heat. Stir in the onion, green pepper, and jalapeno pepper. Sauté until onions are lightly browned, about 10 minutes. Transfer vegetables to a plate and set aside. Do not clean the pan.
Heat remaining oil in the pan over high heat until hot. Add chicken and cook until slightly browned, 1 to 4 minutes, depending on thinness. With a slotted spoon, transfer chicken to a plate.
Place a tortilla on each of 4 plates. Add one-fourth of the chicken to each in a narrow band, leaving a 1-inch margin at each end of the tortilla. Top chicken with one-fourth of the vegetables, then one-fourth of the salsa, then one-fourth of the cilantro. Fold ends of the tortilla over the filling. Roll up as tightly as possible. Serve immediately.