At the end of inflation the Universe is frozen in a near zero-entropy state with energy density in a coherent scalar field and must be ``defrosted'' to produce the observed entropy and baryon number. We propose that the baryon asymmetry is generated by the decay of supermassive grand-unified-theory (GUT) bosons produced nonthermally in a preheating phase after inflation. We show that baryogenesis is possible for an inflaton mass of order ${10}^{13}\mathrm{GeV}$ and a GUT Higgs boson mass of order ${10}^{14}\mathrm{GeV}$, thus solving many drawbacks facing GUT baryogenesis in the old reheating scenario.