In 12x8-inch (2-quart) glass baking dish or large resealable food storage plastic bag, combine vinegar, apple juice, brown sugar, soy sauce, oil, dry mustard and pepper; mix well. Add ribs, turning to coat. Cover dish or seal bag. Refrigerate at least 8 hours or up to 24 hours to marinate.
Heat gas or charcoal grill for indirect cooking as directed by manufacturer or see p. 40 (Kitchen Tip). When grill is heated, remove ribs from marinade; reserve and refrigerate marinade. Place ribs on grill directly over drip pan. Cover grill; cook 2 to 2 1/4 hours or until tender, turning occasionally.
During last 30 minutes of cooking time, in small saucepan, combine reserved marinade and chili sauce; mix well. Bring to a boil. Reduce heat to medium-low; simmer 20 to 30 minutes or until slightly thickened and reduced, stirring occasionally. (Sauce will be similar to syrup.) Serve sauce with ribs. Sprinkle ribs with parsley.