The first measurement of the lifetime of the doubly charmed baryon Xi(++)(cc) is presented, with the signal reconstructed in the final state Lambda K-+(c)-pi(+)pi(+). 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 Xi(++)(cc) lifetime is measured to be 0.256(-0.022)(+0.024) (stat) +/- 0.014(syst) ps.