Prepare the grill for direct cooking over medium heat (350° to 450°F).
In a medium bowl combine the oil, rosemary, salt, and pepper. Add the potatoes and stir to coat them evenly. Brush the cooking grates clean. Grill the potatoes over direct medium heat, with the lid closed as much as possible, until tender and browned on all sides, 15 to 20 minutes, scooping and turning with a wide spatula every 5 minutes or so. Remove from the grill and transfer the potatoes to a serving bowl. Serve warm.