Differential-chaos-shift-keying　cooperative　communication　(DCSK-CC)　has　attracted　a　great　deal　of　attention　in　the　past　five　years,　because　it　can　overcome　the　negative　effect　of　wireless　multipath　fading.　However,　the　conventional　DCSK-CC　system　suffers　from　a　major　disadvantage　of　low　data　rate　due　to　the　resource　consumption　in　cooperation.　To　address　the　issue,　this　paper　proposes　an　efficient　cooperative　scheme,　called　partial-sequence　CC　(PS-CC)　scheme,　for　the　DCSK-CC　system.　In　the　PS-CC　framework,　the　source　and　relays　only　transmit　a　partial　chaotic　sequence　corresponding　to　one　bit　to　the　destination,　while　consuming　the　same　transmission　energy　as　DCSK-CC.　To　validate　the　feasibility　of　the　DCSK　PS-CC　system,　this　paper　carries　out　the　error　performance,　diversity　order,　and　data　rate　analyses　under　different　cooperative　conditions　over　multipath　fading　channels.　Both　numerical　and　simulated　results　show　that　the　proposed　PS-CC　system　outperforms　the　DCSK-based　non-cooperative　system　and　DCSK-CC　systems　over　the　range　of　signal-to-noise　ratio　under　study.　Moreover,　the　proposed　system　can　enhance　data　rate　and　reduce　the　computational　overhead　of　the　relays　as　compared　with　the　DCSK-CC　system.　In　addition,　it　will　be　demonstrated　that　the　DCSK　PS-CC　system　preserves　its　advantages　in　typical　ultra-wideband　(UWB)　channels.　Overall,　the　PS-CC　appears　to　be　a　desirable　cooperative　scheme　for　those　applications　featured　by　high-data-rate,　low-power,　and　low-complexity,　such　as　wireless　sensor　networks　using　the　transmitted　reference　UWB　technique.