This paper proposes an innovative chaotic circuit based on Chua's oscillator. It combines traditional realization of a non-linear resistor in Chua's chaotic oscillator with a promising memristive circuitry. This mixed implementation connects old research works that were focused on diodes with relatively new research papers that are, now, concentrated on memristors. As a result, more reliable chaotic circuit with an HP memristor is obtained that could be used as a source of randomness. Dynamic behavior of the circuit is studied by obtaining fft analysis, different chaotic attractors and Lyapunov exponent spectrum. The results show that the addition of a memristor enhances chaotic behavior of the circuit while maintaining the same power dissipation.