By allowing almost arbitrary distributions of amplitude and phase of electromagnetic waves to be generated by a layer of sub-wavelength-size unit cells, metasurfaces have given rise to the field of meta-holography. However, holography with circularly polarized waves remains complicated as the achiral building blocks of existing meta-holograms inevitably contribute to holographic images generated by both left-handed and right-handed waves. Here we demonstrate how planar chirality enables the fully independent realization of high-efficiency meta-holograms for one circular polarization or the other. Such circular-polarization-selective meta-holograms are based on chiral building blocks that reflect either left-handed or right-handed circularly polarized waves with an orientation-dependent phase. Using terahertz waves, we experimentally demonstrate that this allows the straightforward design of reflective phase meta-holograms, where the use of alternating structures of opposite handedness yields independent holographic images for circularly polarized waves of opposite handedness with negligible polarization cross-talk.