All-solid-state lithium-ion batteries employing solid-state electrolytes promise higher operational safety, enhanced temperature stability, potentially higher cell voltages, and consequently higher energy density compared to traditional batteries with liquid electrolytes based on flammable organic solvents. So far, only a few oxide- and thiophosphate-based solid-state electrolytes exhibit lithium ion conductivities near room temperature comparable to liquid organic electrolytes. However, none of these electrolytes has enabled the fabrication of a competitive all-solid-state battery yet. Here we report the discovery of a superionic phase near room temperature in the class of lithium amide-borohydrides, enabling ionic conductivities of 8 mS/cm near room temperature, comparable to values of common organic liquid electrolytes. The transition into the superionic phase is demonstrated to be triggered by melting of a fully occupied lithium sublattice into a symmetry-equivalent interpenetrating dual sublattice consisting of lithium vacancy sites. We further demonstrate excellent rate performance up to 5C and stable cycling over 400 cycles at 1C of our solid-state electrolytes in half-cell battery configuration representing an important step towards a viable solid-state battery technology.