In a small bowl whisk together Dijon mustard, brown sugar, apple juice, and Worcestershire sauce until smooth. Pour 2/3 of the sauce into a sealable plastic bag. Cover and refrigerate the remaining 1/3 of the sauce. Add the pork chops to the plastic bag, coat with the marinade and seal the bag. Place into the refrigerator and marinate for 8 hours to overnight.
Remove the pork chops from the bag and discard the marinade.
Lightly grease the grates of an outdoor grill. Heat the grill to medium-high heat. Place the pork chops onto the grill, and cook while basting with the reserved marinade for 4-5 minutes per side until fully cooked (the internal temperature has reached 145 degrees F). Let the pork stand for 5 minutes before serving.