  A two dimensional array of Josephson junctions in a magnetic field is
considered. It is shown that the dynamics of the vortices in the array
resembles that of electrons on a two--dimensional lattice put in a magnetic
field perpendicular to the lattice. Under appropriate conditions, this
resemblance results in the formation of a quantum Hall fluid of vortices. The
bosonic nature of vortices and their long range logarithmic interaction make
some of the properties of the vortices' quantum Hall fluid different from those
of the electronic one. Some of these differences are studied in detail.
Finally, it is shown that a quantum Hall fluid of vortices manifests itself in
a quantized Hall electronic transport in the array.
