Yes, you can make potato chips without a deep fryer contrary to what Tim seems to think. These were so easy to make using a mandolin with the thin slice attachment and a baking stone. These are also delicious, and crispy!
What you'll need:
Potatoes (I used gold potatoes, but you could use russet as well)
Pre-heat your oven to 350 degrees.
Scrub your potatoes well, but leave the skins on. Slice potatoes very thinly. Brush a thin layer of olive oil over a couple of baking stones (the number of baking stones you need will depend on how many potatoes you have so do this as you go).
Lay potato slices on the baking stone in a single layer and so that none of the potatoes are touching each other.
Bake the potato slices for about 10 minutes. Pull them out, flip them over,
and return them to the oven until crispy. This will be another 10 minutes probably. You want to keep a close eye on them. I was multi-tasking so some of mine burned.