Boil the potatoes in the skins in salted water for about 10 minutes, then drain and cut in half.
Halve the chorizo slices. Peel and finely chop the garlic, then stir in the olive oil.
Brush the cut side of the potatoes with garlic oil. Place half a slice of chorizo between 2 potato halves and stick 5 chorizo potatoes on a wooden skewer. Grill the skewers on the edge of a grill for about 10 minutes, turning them several times, brushing with the remaining oil.