Preheat grill to medium. Peel back the husks of the corn without removing them. Remove the silks and recover the corn with the husk. Soak in large bowl of cold water for 30 minutes. Remove corn from water and shake off excess. Place the corn on the grill, close the cover and grill for 15 to 20 minutes.
Unwrap corn and brush with the garlic butter. Sprinkle with the cotija cheese and squeeze with lime. Sprinkle with chopped chives, to garnish.