  We present a mechanism to generate the baryon asymmetry of the Universe which
preserves the net baryon number created in the Big Bang. If dark matter
particles carry baryon number $B_X$, and $\sigma^{\rm annih}_{\bar{X}} <
\sigma^{\rm annih}_{X} $, the $\bar{X}$'s freeze out at a higher temperature
and have a larger relic density than $X$'s. If $m_X \lsi 4.5 B_X $GeV and the
annihilation cross sections differ by $\mathcal{O}$(10%) or more, this type of
scenario naturally explains the observed $\Omega_{DM} \approx 5 \Omega_b$. Two
concrete examples are given, one of which can be excluded on observational
grounds.
