We report the first measurement of the absolute branching fraction for Λ_{c}^{+}→Λe^{+}ν_{e}. This measurement is based on 567 pb^{-1} of e^{+}e^{-} annihilation data produced at sqrt[s]=4.599 GeV, which is just above the Λ_{c}^{+}Λ[over ¯]_{c}^{-} threshold. The data were collected with the BESIII detector at the BEPCII storage rings. The branching fraction is determined to be B(Λ_{c}^{+}→Λe^{+}ν_{e})=[3.63±0.38(stat)±0.20(syst)]%, representing a significant improvement in precision over the current indirect determination. As the branching fraction for Λ_{c}^{+}→Λe^{+}ν_{e} is the benchmark for those of other Λ_{c}^{+} semileptonic channels, our result provides a unique test of different theoretical models, which is the most stringent to date.