In a small bowl, stir together the miso, honey, mustard, and pepper with 2 tablespoons water. Place the chicken and half the marinade in a gallon-size ziplock bag. Seal the bag, then massage and turn it to evenly coat the chicken. Refrigerate 30 minutes or overnight. Refrigerate the remaining marinade in a separate container.
Prepare your grill for cooking over medium-high heat. Generously oil the grill grates. Grill the chicken, covered, 3 minutes on each side. Baste the chicken with the reserved marinade, then grill it until the internal temperature reaches 165°, 2 to 3 minutes more per side.