Prepare the chicken marinade. Combine ½ cup Italian dressing, juice and zest of 2 limes, 2 cloves garlic (minced or grated), 1 tsp cumin, ½ tsp chili powder, and ¼ tsp cayenne.
Place chicken in zip-top bag or other air tight container. Pour in marinade. Seal container and transfer to refrigerator. Marinate at least 2 hours.
When you’re ready to begin cooking, cut onions into strips or petals. Cut bell pepper into similar sizes and place in a bowl. Coat with juice from 1 lime, 1 glove (minced or grated) garlic, and ½ tsp cumin. Set aside until ready to grill.
Grill chicken breasts until cooked all the way through. (Not giving a cooking time here because it’s highly dependent on your grill, the size of the chicken breasts, etc.) Grill veggies at the same time (see next step.)
Grill the veggies in a grill basket or on aluminum foil, turning them periodically so they cook evenly and don’t burn on one side.
Once the chicken is cooked all the way through, transfer it to a cutting board and cut it into small strips.
Warm the tortillas either on the grill (heat off or indirect heat) or in the microwave.