In quantum optics, light–matter interaction has conventionally been studied using small atoms interacting with electromagnetic fields with wavelength several orders of magnitude larger than the atomic dimensions1,2. In contrast, here we experimentally demonstrate the vastly different ‘giant atom’ regime, where an artificial atom interacts with acoustic fields with wavelength several orders of magnitude smaller than the atomic dimensions. This is achieved by coupling a superconducting qubit3 to surface acoustic waves at two points with separation on the order of 100 wavelengths. This approach is comparable to controlling the radiation of an atom by attaching it to an antenna. The slow velocity of sound leads to a significant internal time-delay for the field to propagate across the giant atom, giving rise to non-Markovian dynamics4. We demonstrate the non-Markovian character of the giant atom in the frequency spectrum as well as non-exponential relaxation in the time domain.