Season the chicken breasts generously with salt, black pepper, and a light drizzle of olive oil. Rub the seasoning in evenly and set aside while preheating the grill to medium heat (about 10 minutes).

Place the seasoned chicken breasts on the hot grill. Grill for 5 to 7 minutes on one side until they have nice grill marks and are cooked through. Flip the chicken and grill the other side for an additional 5 to 7 minutes.

Layer a slice of ham and a slice of Swiss cheese on each breast when the chicken is almost done. Close the grill lid for about 1-2 minutes to melt the cheese.

While the cheese is melting, place sandwich buns on the grill. Toast for 2-3 minutes until golden brown, flipping halfway for even toasting.

Assemble the sandwich by spreading a layer of Dijon mustard and mayonnaise on the inside of each toasted bun. Place the grilled chicken, ham, and melted cheese on the bottom half and cover with the top bun.

Slice the sandwich in half for easier handling if desired. Serve warm for the best flavor and texture.