  We present a hybrid method for time-dependent particle transport problems
that combines Monte Carlo (MC) estimation with deterministic solutions based on
discrete ordinates. For spatial discretizations, the MC algorithm computes a
piecewise constant solution and the discrete ordinates uses bilinear
discontinuous finite elements. From the hybridization of the problem, the
resulting problem solved by Monte Carlo is scattering free, resulting in a
simple, efficient solution procedure. Between time steps, we use a projection
approach to ``relabel'' collided particles as uncollided particles. From a
series of standard 2-D Cartesian test problems we observe that our hybrid
method has improved accuracy and reduction in computational complexity of
approximately an order of magnitude relative to standard discrete ordinates
solutions.
