Ghost imaging is a technique -- first realized in quantum optics -- in which the image emerges from cross-correlation between particles in two separate beams. One beam passes through the object to a bucket (single-pixel) detector, while the second beams spatial profile is measured by a high resolution (multi-pixel) detector but never interacts with the object. Neither detector can reconstruct the image independently. However, until now ghost imaging has only been demonstrated with photons. Here we report the first realisation of ghost imaging of an object using massive particles. In our experiment, the two beams are formed by correlated pairs of ultracold metastable helium atoms, originating from two colliding Bose-Einstein condensates (BECs) via $s$-wave scattering. We use the higher-order Kapitza-Dirac effect to generate the large number of correlated atom pairs required, enabling the creation of a ghost image with good visibility and sub-millimetre resolution. Future extensions could include ghost interference as well as tests of EPR entantlement and Bells inequalities.