We consider string theory in a time dependent orbifold with a null singularity. The singularity separates a contracting universe from an expanding universe, thus constituting a big crunch followed by a big bang. The theory on the orbifold appears to be well-defined and physically sensible at least to one loop order in string perturbation theory. We quantize the theory both in light-cone gauge and covariantly, and study tree and one loop amplitudes. Our results indicate that strings can pass through the singularity from the contracting to the expanding universe.