We report how a grating interferometer yields neutron dark-field scatter images for tomographic investigations. The image contrast is based on ultrasmall-angle scattering. It provides otherwise inaccessible spatially resolved information about the distribution of micrometer and submicrometer sized structural formations. Three complementary sets of tomographic data corresponding to attenuation, differential phase, and small-angle scattering can be obtained from one measurement. The method is compatible with conventional imaging and provides significantly higher efficiency than existing techniques.