Crystal diffraction is a well-established technique for high-resolution structural analysis of material science and biological samples. However, the recovered structure is a result of averaging over all the unit cells in the crystal, which smears out the imperfections, atomic defects, or asymmetries and chiral properties of the individual molecules. We propose Bragg holography, where a nano-crystal is imaged at a defocus distance allowing separation of the diffracted beams, without turning them into peaks. The presence of a reference wave gives rise to a Bragg hologram, which can be reconstructed by conventional holographic reconstruction algorithms. The recovered complex-valued wavefront contains the complete information about the atomic distribution in the crystal, including defects. Bragg holography is demonstrated for gold nano-crystals, and its feasibility for biological nano-crystals is shown.