Preheat the oven to 225 degrees F. Line two baking sheets with parchment paper.
Slice the zucchini thinly (1/8-inch thick or less), either by hand or on a mandoline. Lay the slices in single layer on paper towels and pat dry.
Whisk together the olive oil, vinegar and salt in a medium bowl. Add the zucchini and toss to coat. Spread the slices on the prepared baking sheets in a single layer without touching. Season with salt.
Bake, rotating the trays from top to bottom every 20 minutes, until the zucchini slices are very crisp, about 1 hour 15 minutes. While still hot, toss the chips with the paprika.
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