In　this　letter,　we　propose　a　reconfigurable　intelligent　surface　(RIS)-aided　dual　M-ary　differential　chaos　shift　keying　(RIS-DM-DCSK)　system　for　non-coherent　chaotic　communications.　In　RIS-DM-DCSK,　a　dual　M-ary　DCSK　signal　is　designed　to　transmit　twice　the　number　of　modulated　bits　compared　to　a　standard　M-ary　DCSK　signal　while　permutation　index　modulation　is　employed　to　convey　additional　index　bits,　thereby　enhancing　energy　efficiency.　Furthermore,　we　propose　a　permutation　index　detection　and　dual　M-ary　DCSK　demodulation　algorithm　to　recover　the　transmitted　bits.　The　bit　error　probability　(BEP)　of　RIS-DM-DCSK　is　analyzed　over　a　Rayleigh　fading　channel.　Numerical　results　show　that　the　proposed　RIS-DM-DCSK　achieves　superior　bit　error　rate　(BER)　performance　and　energy　efficiency　compared　to　benchmark　schemes.　©　2024　IEEE.　All　rights　reserved.