  We examine the possibility of observing Bose condensation of a confined
two-dimensional polariton gas in an organic quantum well. We deduce a suitable
parameterization of a model Hamiltonian based upon the cavity geometry, the
biexciton binding energy, and similar spectroscopic and structural data. By
converting the sum-over-states to a semiclassical integration over
$d$-dimensional phase space, we show that while an ideal 2-D Bose gas will not
undergo condensation, an interacting gas with the Bogoliubov dispersion
$H(p)\approx s p$ close to $p=0$ will undergo Bose condensation at a given
critical density and temperature. We show that $T_c/\sqrt{\rho_c}$ is sensitive
to both the cavity geometry and to the biexciton binding energy. In particular,
for strongly bound biexcitons, the non-linear interaction term appearing in the
Gross-Pitaevskii equation becomes negative and the resulting ground state will
be a localized soliton state rather than a delocalized Bose condensate.
