In a cold skillet, place the chicken skin in one layer. Turn the heat to medium-low. Cook the skin, turning often, until the skin is rich golden brown and completely crispy, 35 to 45 minutes.
Using tongs, remove the crispy skin from the pan, letting any excess oil drip back into the pan. Transfer the skin to a small baking sheet or glass container and reserve for another use. Pour the rendered chicken fat from the pan into a glass jar with a lid.