Electromagnetic reverberation chambers are now commonly used in the domain of ElectroMagnetic Compatibility (EMC) where electronic devices or wirelessly connected objects are, for instance, submitted to immunity tests. By modifying the standard geometry of current reverberation chambers-which are metallic Faraday cavities-to make them chaotic, we have shown that the statistical requirements of a well-operating reverberation chamber are better satisfied in the more complex geometry due to its spatial and spectral statistical behaviors being very close to those predicted by random matrix theory. More specifically, we have shown that in the range of frequency corresponding to the first few hundred modes, the suppression of non-generic modes could be achieved by drastically reducing the amount of parallel walls. Among other results we could demonstrate that, in a chaotic cavity, the low frequency limit of a well operating reverberation chamber can be significantly reduced under the usual values met in conventional mode-stirred reverberation chambers.