In the seesaw model, the baryon asymmetry of the Universe can be generated by the decay of the lightest right-handed neutrino, nu_R. For a hierarchical spectrum of right-handed neutrinos, we show that there is a model independent upper bound on the CP asymmetry produced in these decays: epsilon < 3 m_{nu_3} M_{nu_R}/(8 pi ^2). This implies that epsilon and the mass M_{nu_R} of the lightest right-handed neutrino are not independent parameters, as is commonly assumed. If m_{nu_3} = sqrt{Delta m^2_{atm}} and the nu_R are produced thermally, then leptogenesis requires a reheat temperature of the Universe T_{reh} > M_{nu_R} > 10^8 GeV. Reasonable estimates of nu_R production and the subsequent washout of the asymmetry, as made by Buchmuller and Plumacher, imply M_{nu_R} > 10^9 GeV, and T_{reh} > 10^{10} GeV. Implications for the gravitino problem are also discussed.