Add butter, 1/2 tablespoon chives and 1/4 cup gorgonzola to a bowl. Stir together. Lay out a piece of plastic wrap. Dollop butter onto plastic and fold both long sides over the butter and roll into a log about the same size as a stick of butter. Twist ends and place in refrigerator.
Preheat grill to medium heat. Meanwhile, cut 4 squares of foil large enough to wrap the ears of corn. Place each ear on a piece of foil and season with salt and pepper.
Cut butter into 12 equal slices. Add two slices to each piece of corn then wrap tightly. Set 4 remaining slices aside for later.
Place wrapped corn on the grill and cook for 15 minutes, flipping every 5 minutes. Carefully unwrap the corn and top each with another slice of butter. Garnish with extra chives and gorgonzola.