This paper aims to propose a multiuser OFDM system with non-coherent differential quadrature chaos-shift-keying (OFDM-DQCSK) modulation. The proposed system is based on direct sequence spread spectrum where chaotic codes replace conventional spreading sequences. Orthogonal sets of chaotic spreading codes can be generated. The proposed system uses duplicated reference subcarriers that are private and non-shared. At the receiver, these reference subcarriers are used for the differential non-coherent de-spreading. Neither complex channel estimators nor carrier synchronization is required for demodulation. The chaotic reference signals are averaged at the receiver so that the additive white gaussian noise (AWGN) on the reference signal is averaged to a negligible value. A simulation of the bit error rate performance is performed in the presence of AWGN, multipath Rayleigh flat-fading channels and multiple access interference (MAI). In conclusion, the proposed non-coherent system achieves a remarkable improvement due to the usage of the Reference Averaging Technique.