This　paper　investigates　the　performance　of　non　binary　low-density　parity-check　(LDPC)　channel　coded　M-ary　differential　chaos　shift　keying　(DCSK)　modulation　systems　over　Rayleigh　fading　channels.　The　receiver　adopts　non-coherent　detector　for　DCSK　modulation　and　sum-product　algorithm　(SPA)　for　channel　coding.　Unlike　that　the　previous　binary　channel　coded　M-ary　DCSK　system　uses　turbo　iterative　decoding　between　the　detector　and　the　channel　decoder,　the　nonbinary　coded　DCSK　system　does　not　require　turbo　iteration,　which　simplifies　the　receiver　implementation　and　reduces　the　decoding　latency,　because　that　soft　information　from　M-ary　detector　can　be　directly　used　by　M-ary　channel　decoder.　The　simulation　result　shows　that　the　proposed　nonbinary　coded　M-ary　DCSK　system　has　much　better　error　performance　than　the　binary　coded　one.