Preheat oven to 300 degrees F.
Brush alligator ribs with enough barbecue sauce to coat. Place ribs on a rack set in a baking pan. Cover with plastic wrap and then aluminum foil. Bake for 3 hours.
Remove alligator ribs from the oven. When cool enough to handle, remove the plastic wrap and cover loosely with the aluminum foil; allow the ribs to rest 20 to 30 minutes.
Meanwhile, prepare a smoker with your favorite type of wood chips. Transfer the ribs to the smoker and smoke for 30 to 45 minutes, depending on the size of the ribs; alligator ribs are very lean and dry out easily, so you may want to remove smaller ribs from the smoker first. After smoking, coat the ribs with more barbecue sauce.
While ribs are smoking, preheat a grill to medium-high. Place ribs on the grill and grill just until sauce begins to caramelize. Serve immediately.
This recipe was provided by a chef, restaurant or culinary professional. It has not been tested for home use.