I found this recipe in a special insert to my local paper (years ago), but only just recently tried it. I thought there wasn't anything you could do new to a potato, but I was so wrong! Friends and family also recommended the aioli mix over fish. . .
In a large pot of salted water, boil potatoes until just thoroughly cooked, but not completely soft, 10 - 15 minutes depending on size. Test by piercing a potato with a thin skewer; when the skewer meats some resistance but can slide all the way through, the potatoes are ready. Drain potatoes immediately and set aside until cool enough to handle.
Combine mayonnaise, garlic, lemon juice, lemon rind, 1/4 tsp salt and 1/4 tsp pepper in a blender; blend until smooth.
Heat grill to high.
Cut potatoes in half, brush the cut sides with oil, and season with remaining 1/4 tsp salt and 1/4 tsp pepper. Grill potatoes cut side down until golden brown and just thoroughly cooked, 2 - 3 minutes.
Place potatoes on a platter, drizzle with the aioli and sprinkle with chives.