1. Trim and discard fat and any silvery membrane from pork. Sprinkle meat lightly with salt and pepper, and as much cayenne as you like.
2. Set a 10- to 12-inch frying pan over high heat. When hot, add oil and swirl to coat pan. Add pork and brown on all sides, turning as needed, about 4 minutes total.
3. Transfer meat to a 9- by 13-inch pan. Bake in a 400° oven until a thermometer inserted in center of thickest part of meat registers 155°, about 15 minutes. Put meat on a platter, and let stand for 5 minutes.
4. Meanwhile, add rum to the unwashed frying pan. Stir over medium heat to free browned bits, then pour these drippings into the roasting pan. Stir over low heat, mixing in chutney, until hot.
5. Cut pork on the diagonal into 1/2-inch-thick slices. Accompany with the chutney and salt and pepper to taste.