  We consider the quantum melting of a two-dimensional flux lattice at
temperature T = 0 in the ``superclean limit.'' In this regime, we find that
vortex motion is dominated by the Magnus force. A Lindemann criterion predicts
melting when $n_v/n_p \geq \beta$, where $n_v$ and $n_p$ are the areal number
densities of vortex pancakes and Cooper pairs, and $\beta \approx 0.1$. A
second criterion is derived by using Wigner crystal and Laughlin wave functions
for the solid and liquid phases respectively, and setting the two energies
equal. This gives a melting value similar to the Lindemann result. We discuss
the numerical value of the melting field at $T = 0$ for thin layers of
low-T$_c$ superconductor, such as $a-MoGe$, and single layers of high-T$_c$
materials.
