The celebrated Hong, Ou and Mandel (HOM) effect is one of the simplest illustrations of two-particle interference, and is unique to the quantum. In the original experiment, two photons arriving simultaneously in the input channels of a beam-splitter were observed to always emerge together in one of the output channels. Here, we report on the realization of a closely analogous experiment with atoms instead of photons. This opens the prospect of testing Bell’s inequalities involving mechanical observables of massive particles, such as momentum, using methods inspired by quantum optics, with an eye on theories of the quantum-to-classical transition. Our work also demonstrates a new way to produce and benchmark twin-atom pairs that may be of interest for quantum information processing and quantum simulation.