Models of particle acceleration in solar eruptive events suggest that roughly equal energy may go into accelerating electrons and ions. However, while previous solar X-ray spectroscopic imagers have transformed our understanding of electron acceleration, only one resolved image of γ-ray emission from solar accelerated ions has ever been produced. This paper outlines a new satellite instrument concept—the large imaging spectrometer for solar accelerated nuclei (LISSAN)—with the capability not only to observe hundreds of events over its lifetime, but also to capture multiple images per event, thereby imaging the dynamics of solar accelerated ions for the first time. LISSAN provides spectroscopic imaging at photon energies of 40 keV–100 MeV on timescales of ≲10 s with greater sensitivity and imaging capability than its predecessors. This is achieved by deploying high-resolution scintillator detectors and indirect Fourier imaging techniques. LISSAN is suitable for inclusion in a multi-instrument platform such as an ESA M-class mission or as a smaller standalone mission. Without the observations that LISSAN can provide, our understanding of solar particle acceleration, and hence the space weather events with which it is often associated, cannot be complete.