  In this note we demonstrate that vortices in a non-relativistic Chern-Simons
theory form a quantum Hall fluid. We show that the vortex dynamics is
controlled by the matrix mechanics previously proposed by Polychronakos as a
description of the quantum Hall droplet. As the number of vortices becomes
large, they fill the plane and a hydrodynamic treatment becomes possible,
resulting in the non-commutative theory of Susskind. Key to the story is the
recent D-brane realisation of vortices and their moduli spaces.
