Focussed Ion Beam (FIB) milling is a mainstay of nano-scale machining. By manipulating a tightly focussed beam of energetic ions, often gallium (Ga+), FIB can sculpt nanostructures via localised sputtering. This ability to cut solid matter on the nano-scale has revolutionised sample preparation across the life-, earth- and materials sciences. For example FIB is central to microchip prototyping, 3D material analysis, targeted electron microscopy sample extraction and the nanotechnology behind size-dependent material properties. Despite its widespread usage, detailed understanding of the functional consequences of FIB-induced structural damage, intrinsic to the technique, remains elusive. Here, we present nano-scale measurements of three-dimensional, FIB-induced lattice strains, probed using Bragg Coherent X-ray Diffraction Imaging (BCDI). We observe that even low gallium ion doses, typical of FIB imaging, cause substantial lattice distortions. At higher doses, extended self-organised defect structures appear, giving rise to stresses far in excess of the bulk yield limit. Combined with detailed numerical calculations, these observations provide fundamental insight into the nature of the damage created and the structural instabilities that lead to a surprisingly inhomogeneous morphology.