A chaotic oscillator based on the memristor is analyzed from a chaos theory viewpoint. Sensitivity to initial conditions is studied by considering a nonlinear model of the system, and also a new chaos analysis methodology based on the energy distribution is presented using the Discrete Wavelet Transform (DWT). Then, using Advance Design System (ADS) software, implementation of chaotic oscillator based on the memristor is considered. Simulation results are provided to show the main points of the paper.