Chaotic　modulation　has　attracted　much　attention　in　the　past　two　decades　for　low-power　and　low-cost　wireless　communication　applications　due　to　its　excellent　anti-fading　capability.　In　this　paper,　we　propose　a　new　differential　chaos　shift　keying　(DCSK)-based　system　equipped　with　a　novel　automatic　repeat　request/cooperative　automatic　repeat　request　(ARQ/CARQ)　technique,　called　as　DCSK-ARQ/CARQ　system.　We　also　modify　the　receiver　to　implement　the　DCSK-ARQ/CARQ　system.　To　conduct　a　more　insightful　study,　we　analyze　the　error　performance　and　throughput　of　the　proposed　system　over　multipath　Nakagami-m　fading　channels.　Both　the　theoretical　analyses　and　simulated　results　indicate　that　the　DCSK-ARQ/CARQ　system　is　remarkably　superior　to　the　existing　DCSK　non-cooperative/cooperative　communication　(DCSK-NC/CC)　system.　Moreover,　the　impact　of　various　critical　parameters　on　the　system　performance　is　discussed　and　optimized　so　as　to　facilitate　the　practical　wireless　applications.