In theories where B - L is a spontaneously broken local symmetry, the cosmological baryon asymmetry can be generated by the out-of-equilibrium decay of heavy Majorana neutrinos. We study this mechanism assuming a similar pattern of mixings and masses for leptons and quarks, as suggested by SO(10) unification. This implies that B - L is broken at the unification scale Lambda(GUT) similar to 10(16) GeV, if m(nu mu) similar to 3.10(-3) eV as preferred by the MSW explanation of the solar neutrino deficit. The observed value of the baryon asymmetry, n(B)/s similar to 10(-10), is then obtained without any fine tuning of parameters.