  We study the Quantum Field Theory of nonrelativistic bosons coupled to a
Chern--Simons gauge field at nonzero particle density. This field theory is
relevant to the study of anyon superconductors in which the anyons are
described as {\bf bosons} with a statistical interaction. We show that it is
possible to find a mean field solution to the equations of motion for this
system which has some of the features of bose condensation. The mean field
solution consists of a lattice of vortices each carrying a single quantum of
statistical magnetic flux. We speculate on the effects of the quantum
corrections to this mean field solution. We argue that the mean field solution
is only stable under quantum corrections if the Chern--Simons coefficient
$N=2\pi\theta/g^2$ is an integer. Consequences for anyon superconductivity are
presented. A simple explanation for the Meissner effect in this system is
discussed.
