Active, driven systems as diverse as flocking starlings, swarming bacteria, and vibrating granular beds are by definition non-equilibrium, lacking a well defined thermal temperature that characterizes their dynamics. Because of this, the creation of a coherent non-equilibrium statistical mechanics has proven elusive, and it remains unclear whether, for any non-equilibrium system, a meaningful effective temperature exists. We have constructed an active, driven system of chaotic faraday waves whose statistical mechanics, we find, are surprisingly simple, mimicking those of a thermal ideal gas. We use real-time tracking of a single floating probe, energy equipartition, and the Stokes-Einstein relation to define and measure a pseudotemperature, diffusion constant, and coefficient of viscous friction for a test particle in this pseudothermal gas. Because of its simplicity this system serves as a starting point for direct experimental investigation of non-equilibrium statistical mechanics, much as the ideal gas is the starting point for equilibrium statistical mechanics.