In a small bowl combine ingredients, excluding oysters, mashing them with a fork. Lay a sheet of plastic wrap, place butter mixture in the center and form into a small log. Seal well and refrigerate at least 1 hour (or freeze up to month).
Heat grill to medium high. Place oysters on grate, cup side down. (Oyster shells have one flat side, one cupped side.) Grill 3 to 4 minutes. Remove with tongs and place onto a folded kitchen towel. With an oyster knife, remove and discard top shell (be careful not to lose the liquid inside).
Separate oyster from bottom shell, but do not remove. Place about 1 teaspoon of butter mixture on top of each oyster. Place oysters back on grill grateand cook 2 to 3 minutes more -- the edges of the oysters will start to curl when they are ready. Remove from grill and serve immediately.