Preheat the oven to 350 degrees F. Line a Large cookie sheet with aluminun foil and spray with non-stick cooking spray.
Slice the chicken breast lengthwise down the side to butterfly the chicken breast. Open the chicken breast and inside place 2 slices of ham and 1 slice of Swiss cheese. Fold over and place chicken aside, repeat with other chicken breast.
In a medium bowl, beat eggs. In two separate plates pour flour in one plate and bread crumbs in another. Dip the stuffed chicken breast in flour and lighly coat. Next, dip chicken in egg mixture, then in bread crumbs until completely coated.
Place on prepared cookie sheet. Repeat with the other stuffed chicken breast. Bake in oven for 25 to 30 minutes or until fully cooked.
In a small sauce pan heat the gravy. Once chicken is done, place the chicken on a plate and pour gravy over the top.