Step 1Slice the chicken on the diagonal into quarter-inch slices (which will range in thickness up to 1 or 2 inches). Cut the slices lengthwise into quarter-inch strips. Combine the chicken in a shallow glass dish with the juice of one lime half, the garlic, 1 teaspoon Worcestershire sauce and the salt. Cover and marinate while preparing remaining ingredients.
Step 2Cut the onions in half lengthwise, then slice lengthwise into quarter-inch strips. Set aside. Cut the pasilla peppers in half lengthwise then remove stems and seeds. Slice them into quarter-inch strips and set aside. Repeat with the bell peppers. (Keep the three vegetables separate.)
Step 3Heat 2 tablespoons of the oil in a 14-inch skillet over medium-high heat until hot. Add the onions and saute, stirring occasionally, until golden with browned spots, about 10 minutes. Spoon the cooked onions into a large bowl. Repeat with the pasilla pepper strips and the red pepper strips, adding 2 tablespoons of the oil to the same skillet each time, cooking until tender and browned on the edges, about 10 minutes. Add to the bowl of cooked onions.
Step 4Return the peppers and onions to the skillet and season with the cumin, balsamic vinegar, the remaining Worcestershire sauce, the juice of the remaining lime half and salt and pepper to taste. Keep warm over low heat while cooking the chicken.
Step 5Heat 2 tablespoons oil in a large skillet over high heat and saute half the chicken strips until browned around the edges and cooked through, about 5 minutes. Transfer the cooked chicken to the skillet with the peppers and onions. Cook the remaining chicken and add to the skillet. Adjust the seasoning, adding salt or pepper, if needed. Stir in the cilantro. Keep the mixture warm while heating the tortillas.
Step 6Quickly warm the tortillas, one at a time, in a seasoned or lightly oiled skillet or grill pan, 1 to 2 minutes per side. Spoon about 1 cup fajitas down the center of each tortilla. Serve the fajitas with the tortillas open on the plate.