A measurement of the Lambda(0)(b) lifetime using the decay Lambda(0)(b) -> J/psi Lambda in protonproton collisions at root s = 7TeV is presented. The data set, corresponding to an integrated luminosity of about 5 fb(-1), was recorded with the CMS experiment at the Large Hadron Collider using triggers that selected dimuon events in the J/psi mass region. The Lambda(0)(b) lifetime is measured to be 1.503 +/- 0.052 (stat.) +/- 0.031 (syst.) ps