  Sphalerons of a new gauge interaction can convert a primordial asymmetry in B
or L into a dark matter asymmetry. From the equilibrium conditions for the
sphalerons of both the electroweak and the new interactions, one can compute
the ratios of B, L, and X, where X is the dark matter number, thus determining
the mass of the dark matter particle fairly precisely. Such a scenario can
arise naturally in the context of unification with larger groups. An
illustrative model embeddable in $SU(6) \times SU(2) \subset E_6$ is described
as well as an equally simple model based on SU(7).
