  Cooperative ring-exchange is suggested as a mechanism of quantum melting of
vortex lattices in a rapidly-rotating quasi two dimensional atomic
Bose-Einstein condensate (BEC). Using an approach pioneered by Kivelson et al.
[Phys. Rev. Lett. {\bf 56}, 873 (1986)] for the fractional quantized Hall
effect, we calculate the condition for quantum melting instability by
considering large-correlated ring exchanges in a two-dimensional Wigner crystal
of vortices in a strong `pseudomagnetic field' generated by the background
superfluid Bose particles. BEC may be profitably used to address issues of
quantum melting of a pristine Wigner solid devoid of complications of real
solids.
