The structure of chrysotile, an important asbestos mineral, consists of layers curled concentrically or spirally into tubes. Published transmission electron microscope (TEM) images suggest that successive layers are generally stacked out of register with one another. However, a lattice model can be constructed in such a way that each layer can be stacked in register with the next, five times around the circumference, so that the structure exhibits a global 5-fold symmetry. We report here TEM observations confirming that chrysotile asbestos can form crystals with this structure, the first observation of five-fold symmetry in a natural crystalline material.