In a small bowl, combine the sour cream, goat cheese, shallot, lemon juice, chives, 1/4 teaspoon of the salt, and 1/4 cup of water and stir until smooth. Set aside.
Using a mandoline or knife, cut the potatoes lengthwise into very thin slices. In a large bowl, combine the potatoes, oil, and remaining salt and toss well. Heat a grill pan (a cast-iron pan with ridges) over medium heat and add a single layer of potatoes. Cook until golden brown and crispy, 4 to 5 minutes per side. Cook the remaining potatoes in batches. Serve the hot potatoes with the dip.