In a small bowl, combine brown sugar, granulated sugar, salt, black pepper, and paprika. Set aside.
Trim fat from chops. Lightly brush all over with oil. Sprinkle meat all over with rub. Using your hands, gently pat mixture into meat to form a crust, but do not rub hard.
For a charcoal grill, arrange medium-hot coals around a drip pan. Test for medium heat above drip pan. Place chops on the grill rack over drip pan. Cover and grill for 30 to 35 minutes or until done (160 degree F), adding the orange halves, cut sides down, directly over the coals the last 5 minutes of grilling, or until oranges are heated through. (For a gas grill, preheat grill. Reduce heat to medium. Adjust for indirect cooking. Cover and grill as above.)
Remove chops and orange halves from grill. Squeeze juice from half of an orange over each chop. Or, for a more dramatic presentation, serve a chop and an orange half together and let everyone squeeze their own orange juice over their meat. Makes 4 servings.