Galactic cosmic rays (GCRs) are energetic, electrically-charged particles, such as protons, that pervade the galaxy, until now only observed above ~3 MeV because of the impact of penetrating radiation on available low-energy measurements. We have address this challenge, e.g., with new computer simulations of the instrument response, using detailed knowledge of the LECP design, enabling us to newly observe 0.04–1 MeV GCR ions with the Voyager 1 & 2 LECP instruments, in the very local interstellar medium. GCRs have been explained by appealing to acceleration at supernovae shocks, but this new GCR population has a distinct power-law, suprathermal “tail” spectrum, more consistent with acceleration out of a core interstellar plasma population. The angular behavior of the new population is much like the higher energy GCRs, so they do not seem to originate in the heliosphere, and thus are galactic. This new population (1) may resolve a decades-long puzzle from astrochemical studies of diffuse interstellar clouds regarding the level of ionization attributed to traditional GCRs, (2) might generate sufficient pressure to explain the puzzling inability to account for the observed narrowness of the heliosheath, and (3) could help explained the gap between the observed and expected 0.05-MeV energetic neutral atom intensities.