Cover potatoes with cold salted water in a large pot, then bring to a boil. Simmer until slightly resistant in center when pierced with a sharp small knife, 25 to 30 minutes, then transfer to a large bowl of cold water to stop cooking.
Drain well. When cool enough to handle, peel potatoes with a sharp small knife and quarter lengthwise.
Prepare grill for cooking.
Whisk together lime juice, salt, and pepper and add oil in a slow stream, whisking.
Whisk in cilantro.
When fire is hot (you can hold your hand 5 inches above rack for 1 to 2 seconds), grill potatoes in 2 or 3 batches on lightly oiled grill rack (over coals if using a charcoal grill), uncovered, turning, until grill marks appear and potatoes are just tender, 3 to 6 minutes total.
Serve potatoes warm or at room temperature, drizzled with vinaigrette.
·Potatoes can be boiled and peeled 1 day ahead and chilled, covered. ·Vinaigrette can be made 2 hours ahead and kept at room temperature. ·If you aren't able to grill, potatoes can be cooked in a well-seasoned ridged grill pan over moderately high heat, turning, until grill marks appear, 3 to 6 minutes total.
