Combine sour cream, goat cheese, shallot, lemon juice, chives, 1/4 teaspoon salt, and 1/4 cup water in a small bowl.

Stir until smooth to create the chive dip.

Set the chive dip aside.

Using a mandoline or knife, thinly slice the fingerling and purple potatoes lengthwise.

In a large bowl, combine the sliced potatoes, olive oil, and remaining salt.

Toss the potatoes well to coat them evenly with oil and salt.

Heat a grill pan over medium heat.

Add a single layer of potato slices to the hot grill pan.

Cook the potatoes for 4 to 5 minutes per side, until golden brown and crispy.

Repeat with remaining potato slices in batches.

Serve the hot grilled potato chips immediately with the chive dip.