Coherent X-ray microscopy by phase retrieval of Bragg diffraction intensities enables lattice distortions within a crystal to be imaged at nanometre-scale spatial resolutions in three dimensions. While this capability can be used to resolve structure-property relationships at the nanoscale under working conditions, strict data measurement requirements can limit the application of current approaches. Here, we introduce an efficient method of imaging three-dimensional (3D) nanoscale lattice behaviour and strain fields in crystalline materials with a methodology that we call 3D Bragg projection ptychography (3DBPP). This method enables 3D image reconstruction of a crystal volume from a series of two-dimensional X-ray Bragg coherent intensity diffraction patterns measured at a single incident beam angle. Structural information about the sample is encoded along two reciprocal-space directions normal to the Bragg diffracted exit beam, and along the third dimension in real space by the scanning beam. We present our approach with an analytical derivation, a numerical demonstration, and an experimental reconstruction of lattice distortions in a component of a nanoelectronic prototype device.