Wash the potatoes and cook for about 20 minutes in boiling salted water. Peel garlic and chop finely. Remove the thyme leaves. Mix oil, garlic and thyme. Season with salt and pepper.
Drain the potatoes and wrap in aluminium foil. Grill on the hot grill for about 20 minutes. Cut the potatoes crosswise in the aluminium foil and pull them apart a little with two forks. Sprinkle with thyme oil just before serving.