We present direct evidence of dynamical diffraction of x rays from a quasicrystal. High-resolution x-ray-diffraction measurements of the Al-Pd-Mn face-centered icosahedral quasicrystal were performed, revealing a mosaic full width at half maximum of less than 0.001°. In a second experiment, the anomalous transmission of x rays (the Borrmann effect) was observed. These measurements show that nearly perfect quasicrystals may be grown to centimeter-size dimensions allowing x-ray techniques based upon dynamical diffraction to be brought to bear on the analysis of icosahedral structures.