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).

4 pages, Latex (using amsmath,feynmp,graphicx), 4 figures