  We observe the proliferation of vortices in the
Berezinskii-Kosterlitz-Thouless regime on a two-dimensional array of
Josephson-coupled Bose-Einstein condensates. As long as the Josephson
(tunneling) energy J exceeds the thermal energy T, the array is vortex-free.
With decreasing J/T, vortices appear in the system in ever greater numbers. We
confirm thermal activation as the vortex formation mechanism and obtain
information on the size of bound vortex pairs as J/T is varied.
