Bring a large saucepan of salted water to a boil. Add the potatoes and cook over high heat until tender, about 10 minutes. Drain, shaking off any excess water.

Meanwhile, in a large skillet, melt 1 tablespoon of the butter. Add the pancetta and cook over moderate heat, stirring frequently, until just beginning to brown, about 3 minutes. Add the remaining 3 tablespoons of butter and cook, stirring occasionally, until the pancetta is golden and the butter is just beginning to brown, about 2 minutes. Add the shallot and rosemary sprig and cook, stirring, for 2 minutes. Remove the skillet from the heat and discard the rosemary sprig.

Whisk the vinegar and mustard into the pancetta mixture; season with salt and pepper. Add the potatoes and the chives and toss until evenly coated. Serve the potato salad warm or at room temperature.