A large-angle polarization volume grating (PVG) with circular-polarization selectivity is demonstrated using a three-dimensional chiral liquid crystal with simple cubic symmetry - the blue phase (BP) II. We confirm defect-free alignment of the BP crystal on a periodically patterned substrate down to a period of 700 nm, with Kossel diagrams and far-field diffraction patterns suggesting that the lattice becomes slanted within the cell to accommodate to the imprinted pattern. We further demonstrate a tunable PVG by exploiting the external field-responsivity of BPs, making this PVG attractive for a wide range of applications from tunable photonics to augmented reality.