We propose a renormalisable model based on Delta(27) family symmetry with an SO(10) grand unified theory (GUT) leading to a novel form of
spontaneous geometrical CP violation. The symmetries, including Delta(27) and Z_9 x Z_12 x Z_4^R, are broken close to the GUT breaking scale to yield the minimal supersymmetric standard model (MSSM) with the standard R-parity. SO(10) is broken via SU(5) with doublet-triplet splitting achieved by a version of the Dimopoulos-Wilczek (missing VEV) mechanism. Low-scale Yukawa structure is dictated by the coupling of matter to Delta(27) antitriplets whose VEVs are aligned in the CSD3 directions by the superpotential. Light physical Majorana neutrinos masses emerge from a specific implementation of the seesaw mechanism within SO(10). The model predicts a normal neutrino mass hierarchy with the best-fit lightest neutrino mass between 0.32-0.38 meV, CP-violating oscillation phase delta = 275-280 degrees and the remaining neutrino parameters all within 1 sigma of their best-fit experimental values.