Diffraction methods for crystallographic structure determination suffer from the so-called ’phase problem’; a diffraction pattern provides intensity but not phase information for the scattered beams, and therefore cannot be uniquely inverted to obtain the crystal structure of a sample. Holographic methods’, on the other hand, offer a means of extracting both intensity and phase information. To be useful for crystallographic applications, holography must be implemented with radiation of sufficiently small wavelength to resolve atomic-scale features(2). One method, electron-emission holography(3-9), uses electron waves and is a powerful tool for studying surface structure; but it cannot image the internal structure of solids because of complications arising from the highly anisotropic nature of electron scattering processes. A proposed alternative method uses X-rays(2,10-13), which scatter more isotropically than electrons. Here we demonstrate the efficacy of atomic-scale X-ray holography by obtaining direct images of the three-dimensional arrangement of strontium atoms in the cubic perovskite SrTiO3. With more intense synchrotron sources for illumination, and with the development of improved X-ray detectors, X-ray holography should become a powerful general technique for unambiguous structure determination in condensed matter systems.