Preheat the griller to high and put water on to boil. Insert a sprig of rosemary under the skin on each of the chicken thighs.
Scrub the potatoes, put into a saucepan, cover with the boiling water and add a little salt. Bring back to the boil and cook for 15 minutes, until tender.
Meanwhile, arrange the chicken skin side down on the griller rack. Brush with 1 tablespoon oil, sprinkle with salt and black pepper and cook, about 10 cm below the heat for 10 minutes. Turn the thighs over, brush with a further 1 tablespoon oil, season with salt and pepper and cook for 10 minutes more until the skin is golden and crisp. Turn off the griller, but leave the chicken thighs on the rack to keep warm.
While the chicken is cooking, put the remaining oil into a small saucepan. Peel the garlic, crush it into the oil and shake over moderate heat until beginning to sizzle; do not let it colour. Turn off the heat. Beat in the mayonnaise with 2 tablespoons hot water from the kettle until well amalgamated; cover and keep warm.
Drain the potatoes well, slice thickly and return to the saucepan to reheat gently.
Arrange the chicken thighs and potatoes on four individual plates. Spoon a little mayonnaise alongside, then sprinkle with black pepper and serve immediately.