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.