The wave-particle dual nature of light and matter and the fact that the choice of measurement determines which one of these two seemingly incompatible behaviours we observe are examples of the counterintuitive features of quantum mechanics. They are illustrated by Wheeler’s famous `delayed-choice’ experiment, recently demonstrated in a single-photon experiment. Here, we use a single ultracold metastable helium atom in a Mach-Zehnder interferometer to create an atomic analogue of Wheeler’s original proposal. Our experiment confirms Bohr’s view that it does not make sense to ascribe the wave or particle behaviour to a massive particle before the measurement takes place. This result is encouraging for current work towards entanglement and Bell’s theorem tests in macroscopic systems of massive particles.