We present a computer study of an impact oscillator known as the Bender bouncer. It consists of a driven mass on a linear spring, with damping proportional to the velocity, and an infinitely massive, elastic barrier. If it were not for the barrier, the system would be the simple mass on a spring so familiar to students of freshman physics. With the barrier in place, the system displays a remarkable range of behaviors, including energy amplification, chaos, sensitivity to initial conditions, and fractal basins of attraction. The fact that such interesting behavior occurs with such a small modification of a freshman physics problem makes the system especially well suited for presentation to students.