In this paper we design network coding schemes for Differential Chaos Shift Keying (DCSK) modulation. In this work, non-coherent chaos-based communication system is used due to its simplicity and robustness to multipath propagation effects, while dispensing with any channel state information knowledge at the receiver. We propose a relay network using network coding and DCSK, where we first present a Physical layer Network Coding (PNC) scheme with two users, $\mathcal{A}$ and $\mathcal{B}$, sharing the same spreading code and bandwidth, while synchronously transmitting their signals to the relay node $\mathcal{R}$. We show that the main drawback of this design in multipath channels is the high level of interference in the resultant signal, which severely degrades the system performance. Hence, in order to address this problem, we propose two coding schemes, which separate the users' signals in the frequency or the time domains. We show also in this paper that the performance of the Analog Network Coding (ANC) with DCSK modulation suffers from the same interference problem as the PNC scheme. We present the analytical bit error rate performance for multipath Rayleigh fading channel for the different scenarios and we analyse these schemes in terms of complexity, throughput and link spectral efficiency.