Parrotfish (Scaridae) feed by biting stony corals. To investigate how their teeth endure the associated contact stresses, we examine the chemical composition, nano- and microscale structure, and the mechanical properties of the steephead parrotfish Chlorurus microrhinos tooth. Its enameloid is a fluorapatite (Ca₅(PO₄)₃F) biomineral with outstanding mechanical characteristics: the mean elastic modulus is 124 GPa, and the mean hardness near the biting surface is 7.3 GPa, making this one of the stiffest and hardest biominerals measured; the mean indentation yield strength is above 6 GPa, and the mean fracture toughness is ∼2.5 MPa·m^1/2, relatively high for a highly mineralized material. This combination of properties results in high abrasion resistance. Fluorapatite X-ray absorption spectroscopy exhibits linear dichroism at the Ca L-edge, an effect that makes peak intensities vary with crystal orientation, under linearly polarized X-ray illumination. This observation enables polarization-dependent imaging contrast mapping of apatite, a method to quantitatively measure and display nanocrystal orientations in large, pristine arrays of nano- and microcrystalline structures. Parrotfish enameloid consists of 100 nm-wide, microns long crystals co-oriented and assembled into bundles interwoven as the warp and the weave in fabric and therefore termed fibers here. These fibers gradually decrease in average diameter from 5 μm at the back to 2 μm at the tip of the tooth. Intriguingly, this size decrease is spatially correlated with an increase in hardness.