Lay out chicken on a plate. Coat both sides with the oil and place on a preheated grill or grill pan. Cook to an internal temperature of 165 degrees, approximately 3 minutes on each side. Remove from grill and place in hot sauce. Set aside.
Cut celery into small pieces. Peel carrot and shave using a box grater.
Take 8 slices of bread, butter one side and spread blue cheese on the other side. On the blue cheese side, layer mozzarella, chicken, celery, carrots and finish with more mozzarella.
Top with the other piece of bread and place in a nonstick pan on medium heat. Cook for approximately one minute, pressing down with a spatula. Flip and repeat until the cheese is melted and the bread is golden brown. Remove, cut and serve.