Preheat your oven to 375°F.
Wash the outside of the zucchini well and dry. Thinly slice the zucchini crosswise to make lots of thin zucchini chips. I like to slice them about a 1/4 inch in width. Put the zucchini slices into a large bowl and toss with the oil, salt and pepper.
Lay the slices in a single layer on baking trays lined with parchment paper. Using a fine grater such as a microplane, sprinkle the parmesan directly onto the zucchini chips. Put the trays into the oven and bake until the cheese has melted and the zucchini has turned golden and is starting to get crisp at the edges, approximately 15 minutes. Serve immediately.