Unidirectional motion of magnetic domain walls is the key concept underlying next-generation domain-wall-mediated memory and logic devices. Such motion has been achieved either by injecting large electric currents into nanowires or by employing domain-wall tension induced by sophisticated structural modulation. Herein, we demonstrate a new scheme without any current injection or structural modulation. This scheme utilizes the recently discovered chiral domain walls, which exhibit asymmetry in their speed with respect to magnetic fields. Because of this asymmetry, an alternating magnetic field results in the coherent motion of the domain walls in one direction. Such coherent unidirectional motion is achieved even for an array of magnetic bubble domains, enabling the design of a new device prototype-magnetic bubblecade memory-with two-dimensional data-storage capability.