Chicken should always be sliced into strips for fajitas so that the chicken can be browned and crispy on all edges. Traditionally fajitas are cooked in a very hot cast iron pan or comal and part of the appeal is all those caramelized edges that come in contact with the hot pan.
With that said, you can cook whole chicken breasts on the grill or in a cast iron pan and then slice them into thin slices after they have been cooked. We recommend butter-flying the chicken breast for this approach to ensure it can get browned on the outside without burning or overcooking.