Since memristors are widely studied and the range of applications developed for these devices are becoming increasingly broad, circuital implementations exhibiting fingerprints of memristive behavior have become highly relevant. A class of memristor circuits was recently obtained by cascading a static nonlinear two-port with a dynamical one-port. In general, these circuits are classifiable as extended memristors and may be controlled either in current or in voltage. This paper has the aim of presenting a novel element from this class which experiences various complex behaviors, including periodic oscillations and chaos. This thorough investigation of the rich nonlinear dynamics emerging in the proposed circuit may shed light on interesting engineering applications that memristors may be suited for.