  We investigate a small vortex-lattice system of four co-rotating vortices in
an atomic Bose--Einstein condensate and find that the vortex dynamics display
chaotic behaviour after a system quench introduced by reversing the direction
of circulation of a single vortex through a phase-imprinting process. By
tracking the vortex trajectories and Lyapunov exponent, we show the onset of
chaotic dynamics is not immediate, but occurs at later times and is accelerated
by the close-approach and separation of all vortices in a scattering event. The
techniques we develop could potentially be applied to create locally induced
chaotic dynamics in larger lattice systems as a stepping stone to study the
role of chaotic events in turbulent vortex dynamics.
