HEAT your grill until it is nice and hot. This is a quick-cooking dish, so the hotter the better. You want to avoid overcooking, so it's better to work in several smaller batches that you can manage rather than one large batch that might overcook.
SHUCK the oysters.
ARRANGE the shucked oysters on the grill. Discard the top (flatter) shell and arrange the bottom (bowl-like) shells with the raw oysters in rows over the grill.
ADD about a tablespoon of butter to each oyster.
CLOSE the grill and cook the oysters for 3 to 4 minutes. Check them after this time. The oysters should be just barely starting to shrink and you should see some caramelization in the butter around the edges. Cook for another 30 seconds if needed; it's better to undercook the oysters than overcook them.