  In this paper we investigate a possibility for the existence of an analog of
the Quantum Hall Effect for neutral particles with a permanent magnetic moment
$\mu$ in the presence of crossed inhomogeneous magnetic and electric fields. We
predict the appearance of Hall conductivity $\sigma_H=(e^2/h)\nu (\mu)$ with
the Landau filling factor $\nu (\mu)\propto \mu ^2$. The estimates of the model
parameters suggest quite an optimistic possibility to experimentally verify
this prediction in optically trapped clouds of atomic BEC.
