In this paper, we propose a novel non-coherent orthogonal frequency division multiplex (OFDM) based overlapped chaotic chip position shift keying (OCCPSK) system. Different from traditional non coherent chaotic systems, this system endeavors to achieve efficient and secure performances with no need to transmit reference chaotic sequences. At the transmitter, information bits are grouped into multiple subsets and respectively modulated by the position of chaotic chips. Then iterative chaotically shift-aided shuffling and overlapping operations are performed on the resultant multi-ary signals to enhance the security. Subsequently, OFDM modulations are performed and information-bearing signals are transmitted. At the legitimate receiver, with the known key parameters, reverse operations are carried out. Then the positions used for modulations can be formulated out to recover information bits via maximizing the Euclidean norm of received symbols. Since no reference chaotic signals are required to be transmitted, both efficiency and security performances are improved. Moreover, we derive the analytical symbol error rate (SER) and bit error rate (BER) expressions over fading channels, and theoretical spectrum efficiency, energy efficiency and security performances are analyzed. Simulation results verify the effectiveness of derivations, and demonstrate the high efficiency and security of this design.