Remove the outer layer of papery skin from the garlic. Slice off the top 1/2 inch from the pointed top of the garlic head. Set the garlic, cut side up, on a large square of foil. Drizzle it with the olive oil, then wrap the foil up and over it the garlic to form a loose packet.
Set the garlic over the cooler side of the grill and cook for 40 minutes, or until the cloves are golden-brown and soft. Remove from the grill and let cool. To remove the cloves, simply squeeze the entire head (or each clove), and the cloves should pop out of their skins.