  We suggest and experimentally demonstrate a chaotic memory resistor
(memristor). The core of our approach is to use a resistive system whose
equations of motion for its internal state variables are similar to those
describing a particle in a multi-well potential. Using a memristor emulator,
the chaotic memristor is realized and its chaotic properties are measured. A
Poincar\'{e} plot showing chaos is presented for a simple nonautonomous circuit
involving only a voltage source directly connected in series to a memristor and
a standard resistor. We also explore theoretically some details of this system,
plotting the attractor and calculating Lyapunov exponents. The multi-well
potential used resembles that of many nanoscale memristive devices, suggesting
the possibility of chaotic dynamics in other existing memristive systems.
