  The dynamical status of isolated quantum systems, partly due to the linearity
of the Schrodinger equation is unclear: Conventional measures fail to detect
chaos in such systems. However, when quantum systems are subjected to
observation -- as all experimental systems must be -- their dynamics is no
longer linear and, in the appropriate limit(s), the evolution of expectation
values, conditioned on the observations, closely approaches the behavior of
classical trajectories. Here we show, by analyzing a specific example, that
microscopic continuously observed quantum systems, even far from any classical
limit, can have a positive Lyapunov exponent, and thus be truly chaotic.
