The first measurement of the lifetime of the doubly charmed baryon Ξ_{cc}^{++} is presented, with the signal reconstructed in the final state Λ_{c}^{+}K^{-}π^{+}π^{+}. The data sample used corresponds to an integrated luminosity of 1.7 fb^{-1}, collected by the LHCb experiment in proton-proton collisions at a center-of-mass energy of 13 TeV. The Ξ_{cc}^{++} lifetime is measured to be 0.256_{-0.022}^{+0.024}(stat)±0.014(syst) ps.