Preheat oven to 400º. Place chicken on a cutting board and make 5 slits in each breast, being careful not to cut through completely.
In a medium bowl, whisk together mustard, honey, and garlic powder. Season with salt and pepper and rub all over chicken breasts.
Place breasts on a medium cooking tray and stuff each with ham, cheese, and pickle chips.
Bake until chicken is cooked through and no longer pink, 25 minutes. Serve.