  The chiral Abelian Higgs model is studied at finite temperature. By
integrating out the heavy modes, we make a three-dimensional effective theory
for the static modes. It is demonstrated that the plasma masses are correctly
reproduced to leading order in $m^{2}/T^{2}$. The effective potential for the
composite operator $\phi^{\dagger}\phi$ is calculated at one loop for the
resulting three-dimensional theory and it is shown that the result is gauge
parameter invariant. The numerical investigation of the potential reveals that
the symmetry is restored via a first order phase transition. Comparison with
the ordinary ring improved potential is made and it is found that the barrier
height at $T_{c}$ is somewhat higher.
