Synchronization capability of two identical chaotic systems can be used for constructing the secure communication systems where the chaotic signal is used as the information carrier. In this paper, a secure communication system is designed by using the bi-directionally synchronized identical Chua’s circuits in LC parallel coupling. LC parallel circuit is used as the new coupling element instead of using a single resistor or capacitor or inductor as the coupling element. This makes the complete synchronization of Chua’s circuits possible for many different sets of coupling inductance and capacitance values so that the flexibility of constructing the secure communication systems is realized. Both the synchronized Chua’s circuits in LC parallel coupling and the corresponding secure communication system are constructed by using the LTspice software. The simulation results show that the secure communication system proposed in the present paper is very efficient for the message transmission for different pairs of coupling inductance and coupling capacitance values where the complete synchronization of Chua’s circuits is observed occur. The two essential properties of an ideal secure communication system - perfect message masking and recovery are observed when compared to other secure communication systems already proposed and constructed previously. So, the simulation results of the present study can be used for practically constructing the efficient communication systems in future.