Recent large-scale peculiar velocity surveys suggest that large matter volumes could be moving with appreciable velocity with respect to the CMB rest frame. If confirmed, such results could conflict with the Cosmological Principle according to which the matter and CMB rest frames should converge on very large scales. In this work, we explore the possibility that such large-scale bulk flows are due, not to the motion of matter with respect to the CMB, but to the flow of dark energy with respect to matter. Indeed, when dark energy is moving, the usual definition of the CMB rest frame as that in which the CMB dipole vanishes is not appropriate. We find instead that the dipole vanishes for observers at rest with respect to the cosmic center of mass, i.e. in motion with respect to the background radiation.