Peel potatoes and place them in a large pot. Cover with water and season with salt. Bring to a boil and cook over high heat until tender but still firm, 12-20 minutes. Drain.
Preheat a grill to medium heat. When the potatoes are cool enough to handle, cut each lengthwise into 8 wedges. Toss with the oil and sprinkle with paprika, salt and pepper to taste. Place wedges on the grill and cook, turning once, for about 12 minutes or until brown and crispy.