Peel carrots, then slice into strips using the vegetable peeler. Avoid rotating the carrot for as long as possible to make wider sections; the thicker the pieces, the better they will turn out!
Add the carrot strips to a bowl, and toss with olive oil. Start with a smaller amount-- you don't need much! If they seem dry at the full 3 teaspoons, add another teaspoon.
Place carrot peelings in a single layer on the cookie sheet, and sprinkle with salt.
Bake for 10-20 minutes until crispy, tossing once or twice during cooking. (Exact cook time will depend on the thickness of the slices).