We study a model for leptogenesis in which the total $CP$ asymmetries in the decays and scatterings involving the $SU(2)$ singlet seesaw neutrinos ${N}_{\ensuremath{\alpha}}$ vanish (${ϵ}_{{N}_{\ensuremath{\alpha}}}=0$). Leptogenesis is possible due to nonvanishing $CP$ violating lepton flavor asymmetries, realizing a situation in which the baryon asymmetry is due exclusively to flavor effects. We study the production of a net lepton asymmetry by solving the Boltzmann equations specific to this model, and we show that successful leptogenesis can be obtained at a scale as low as the TeV. We also discuss constraints on the model parameter space arising from current experimental upper limits on lepton flavor violating decays.