  We investigate the influence of the Chern-Simons term coupled to the
three-dimensional $x-y$ model. This term endows vortices with an internal
angular momentum and thus gives them arbitrary statistics. The Chern-Simons
term for the $x-y$ model takes an integer value which can be written as a sum
over all vortex lines of the product of the vortex charge and the winding
number of the internal phase angle along that vortex line. We have used the
Monte-Carlo method to study the three-dimensional $x-y$ model with the
Chern-Simons term. Our findings suggest that this model belongs to the $x-y$
universality class with the critical temperature growing with increasing
internal angular momentum.
