A measurement of the Λ0b lifetime using the decay Λ0b→J/ψΛ in protonproton collisions at s√=7 TeV 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/ψ mass region. The Λ0b lifetime is measured to be 1.503 ± 0.052 (stat.) ± 0.031 (syst.) ps.