An all-electronic physical random number generator at rates up to 80 Gbit/s is presented, based on weakly coupled GaAs/Ga0.55Al0.45As superlattices operated at room temperature. It is based on large-amplitude, chaotic current oscillations characterized by a bandwidth of several hundred MHz and do not require external feedback or conversion to an electronic signal prior to digitization. The method is robust and insensitive to external perturbations and its fully electronic implementation suggests scalability and minimal postprocessing in comparison to existing optical implementations.