Preheat the oven to 300F.

Peel the turnips and slice them thinly - a mandoline is the best tool for this task! Discard any imperfect slices as these have a tendency to burn a lot faster. 

Line two large baking sheets with silicone mats and spread the turnip slices out, trying to ensure that they don't overlap. Season with salt, pepper, and cayenne.

Roast for 20 minutes. Once they start to darken at the edges, turn off the oven but leave the turnip chips inside. Keep an eye on them as they will continue to cook. As soon as any start to burn, remove them from the oven. This took about 15 minutes for me.

Leave to cool (they will crisp up further), then store in an airtight container.