We consider a simple class of models in which the relic density of dark matter is determined by the baryon asymmetry of the universe. In these models a $B - L$ asymmetry generated at high temperatures is transfered to the dark matter, which is charged under $B - L$. The interactions that transfer the asymmetry decouple at temperatures above the dark matter mass, freezing in a dark matter asymmetry of order the baryon asymmetry. This explains the observed relation between the baryon and dark matter densities for dark matter mass in the range 5--15 GeV. The symmetric component of the dark matter can annihilate efficiently to light pseudoscalar Higgs particles $a$, or via $t$-channel exchange of new scalar doublets. The first possibility allows for $h^0 \to aa$ decays, while the second predicts a light charged Higgs-like scalar decaying to $����$. Direct detection can arise from Higgs exchange in the first model, or a nonzero magnetic moment in the second. In supersymmetric models, the would-be LSP can decay into pairs of dark matter particles plus standard model particles, possibly with displaced vertices.

22 pages, no figures