ABSTRACT The dynamical influence of binary companions is expected to profoundly influence planetary systems. However, the difficulty of identifying planets in binary systems has left the magnitude of this effect uncertain; despite numerous theoretical hurdles to their formation and survival, at least some binary systems clearly host planets. We present high-resolution imaging of 382 Kepler Objects of Interest (KOIs) obtained using adaptive-optics imaging and nonredundant aperture-mask interferometry on the Keck II telescope. Among the full sample of 506 candidate binary companions to KOIs, we super-resolve some binary systems to projected separations of <5 au, showing that planets might form in these dynamically active environments. However, the full distribution of projected separations for our planet-host sample more broadly reveals a deep paucity of binary companions at solar-system scales. For a field binary population, we should have found 58 binary companions with projected separation < 50 au and mass ratio q > 0.4; we instead only found 23 companions (a 4.6 deficit), many of which must be wider pairs that are only close in projection. When the binary population is parametrized with a semimajor axis cutoff acut and a suppression factor inside that cutoff Sbin, we find with correlated uncertainties that inside au, the planet occurrence rate in binary systems is only times that of wider binaries or single stars. Our results demonstrate that a fifth of all solar-type stars in the Milky Way are disallowed from hosting planetary systems due to the influence of a binary companion.