Preheat oven to 350 degrees, with racks in upper and lower thirds. Peel beets and slice 1/16 inch thick with a mandoline. In a large bowl, toss beets with extra-virgin olive oil.
On two rimmed baking sheets (or use one sheet and bake in two batches), arrange beets in a single layer. Stack another rimmed baking sheet on top of each. Bake until edges of beets begin to dry out, about 20 minutes. Uncover and rotate sheets. Bake 10 to 20 minutes, removing chips as they become lightened in color. Transfer to a wire rack; chips will crisp up as they cool.