A new scenario for generating the Baryon Asymmetry of the Universe is presented. It does not require baryon number violation, it can naturally account for the observed similarity of densities of dark matter and baryonic matter, and the temperature of the Universe need never have been far above the QCD phase transition. If the H dibaryon is compact and lighter than a nucleon plus a Lambda, it would have escaped detection so far and would have a lifetime longer than the age of the Universe. I present a concrete realization of the new scenario in this case.