1. Preheat oven to 350 F, with racks in upper and lower thirds. Peel beets and slice 1/16 inch thick with a mandoline (if you don't have a mandoline, you can also use a vegetable peeler).
2. In a large bowl, toss beets with extra-virgin olive oil. The beets should have a very thin coat. On two rimmed baking sheets (or use one sheet and bake in two batches), arrange beets in a single layer. Sprinkle with a small amount of sea salt.
3. 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 and pale in color. Transfer to a wire rack; chips will crisp up as they cool.