In this work, we provide a practical implementation of a new memristor based chaotic circuit, which was generated by replacing the nonlinear resistor in the canonical Chua's circuit with a flux-controlled memristor. The existence of the chaos is not only demonstrated by computer simulations, but also verified with Lyapunov exponents and bifurcation analysis. Moreover, we present a breadboarded circuit for the implementation of this chaotic circuit, by employing only the four basic circuit elements, the resistor, capacitor, inductor and memristor. Different chaotic attractors are illustrated by both numerical simulations and electronic experiments.