Preheat the oven to 350F.
Slice each chicken breast horizontally to form a pocket.
Brush each ham slice with honey mustard and fold in half. Fold a cheese slice around each ham slice. Insert in pocket of chicken and secure with a toothpick.
Melt butter in a large skillet over medium-high heat. Cook chicken in butter until browned, about 4 minutes per side.
Arrange chicken on a rack in a baking pan. Bake chicken until an instant-read thermometer inserted in center of the meat registers 180F, 15 to 20 minutes.