We present the results of a combined experimental and theoretical investigation of droplets falling onto a horizontal soap film. Both static and vertically vibrated soap films are considered. A quasi-static description of the soap film shape yields a force-displacement relation that allows us to model the film as a nonlinear spring, and yields an accurate criterion for the transition between droplet bouncing and crossing. On the vibrating film, a variety of bouncing behaviors were observed, including simple and complex periodic states, multiperiodicity and chaos. A simple theoretical model is developed that captures the essential physics of the bouncing process, reproducing all observed bouncing states. The system is among the very simplest fluid mechanical chaotic oscillators. The relevance of our model to a seemingly unlikely biological system is discussed.