Butterfly each chicken breast, making sure not to cut all the way through. Sprinkle the inside with Morton's Nature's Seasoning, place the mozzarella cheese, then close the chicken breast. Season the outside with the seasoning as well.
Melt the butter in the microwave. In a small bowl, combine the melted butter, Frank's Red Hot Sauce, celery salt, garlic powder, and cayenne pepper.
Brush one side of the chicken with the hot sauce mixture.
Place chicken hot sauce side down on the grill. Grill for 5-7 minutes, then flip and grill the other side until addition 5-7 minutes. Chicken is done when it reached 165 degrees in the thickest part.