  We describe a "neutrinogenesis" mechanism whereby, in the presence of
right-handed neutrinos with sufficiently small pure Dirac masses,
(B+L)-violating sphaleron processes create the baryon asymmetry of the
Universe, even when B=L=0 initially. It is shown that the resulting neutrino
mass constraints are easily fulfilled by the neutrino masses suggested by
current experiments. We present a simple toy model which uses this mechanism to
produce the observed baryon asymmetry of the Universe. (PostScript Errors
corrected in latest Version).
