We propose an optically rewritable dynamic phase grating based on polymer-templated azo liquid crystal in a blue-phase structure. The grating consists of alternating blue-phase and light-induced isotropic-phase regions, patterned by ultraviolet illumination. In the field-off state, the grating is hidden (showing no diffraction), due to index matching between the two phases. An index change is induced in the blue-phase regions when an external voltage is applied, while the refractive index of the isotropic-phase regions remains the same. The resulting periodic index modulation causes the grating to diffract light. The diffraction efficiency is independent of incident polarization, and the electro-optic response is in the sub-millisecond scale. Enabled by the reversible photoisomerism of the azobenzene, we demonstrate optical-patterning, -erasure, and re-patterning of a single liquid-crystal cell into different grating geometries.