We describe a "neutrinogenesis" mechanism whereby, in the presence of right
-handed neutrinos with sufficiently small pure Dirac masses, (B + L)-violat
ing sphaleron processes create the baryon asymmetry of the Universe, even w
hen B = L = 0 initially. It is shown that the resulting neutrino mass const
raints are easily fulfilled by the neutrino masses suggested by current exp
eriments. We present a simple toy model which uses this mechanism to produc
e the observed baryon asymmetry of the Universe.