Preheat oven to 400 degrees F. Bake the potatoes until fork tender, about 1 hour. Cool, peel, discarding the skins, and break the potatoes into pieces.
Process the almonds, olive oil and garlic in a food processor into a paste. Add the potato chunks, 1/2 cup water, lemon juice, vinegar, 1 1/2 teaspoons salt and a generous grinding of black pepper. Pulse until the mixture just comes together into a thick dip. Take care not to over-process or the dip will be gummy. Season with additional salt and pepper.
Spread the dip on a large serving dish. Drizzle with olive oil and scatter with the chives if using. Serve with vegetables and/or pita chips for dipping.
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