Copper indium diselenide (CIS), along with its derivatives Cu(In,Ga)(Se,S)2, is a prime candidate for use in the absorber layers of photovoltaic devices. Due to its ability to resist radiation damage, it is particularly well suited for use in extraterrestrial and other irradiating environments. However, the nature of its radiation hardness is not well understood. In this study, transmission electron microscopy (TEM) with in situ ion irradiation was used to monitor the dynamic microstructural effects of radiation damage on CIS. Samples were bombarded with 400 keV xenon ions to create large numbers of atomic displacements within the thickness of the TEM samples and thus explore the conditions under which, if any, CIS could be amorphized. By observing the impact of heavily damaging radiation in situ—rather than merely the end-state possible in ex situ experiments—at the magnifications allowed by TEM, it was possible to gain an understanding of the atomistic processes at work and the underlying mechanism that give rise to the radiation hardness of CIS. At 200 K and below, it was found that copper-poor samples could be amorphized and copper-rich samples could not. This difference in behavior is linked to the crystallographic phases that are present at different compositions. Amorphization was found to progress via a combination of one- and two-hit processes. The radiation hardness of CIS is discussed in terms of crystallographic structures/defects and the consequences these have for the ability of the material to recover from the effects of displacing radiation.