  We show that arbitrarily large polar flocks are susceptible to the presence
of a single small obstacle. In a wide region of parameter space, the obstacle
triggers counter-propagating dense bands leading to reversals of the flow. In
very large systems, these bands interact yielding a never-ending chaotic
dynamics that constitutes a new disordered phase of the system. While most of
these results were obtained using simulations of aligning self-propelled
particles, we find similar phenomena at the continuous level, not when
considering the basic Toner-Tu hydrodynamic theory, but in simulations of
truncations of the relevant Boltzmann equation.
