We report a measurement of the lifetime of the Λ0b baryon in decays to the Λ+cπ− final state in a sample corresponding to 1.1  fb−1 collected in pp collisions at s√=1.96  TeV by the CDF II detector at the Tevatron collider. Using a sample of about 3000 fully reconstructed Λ0b events we measure τ(Λ0b)=1.401±0.046(stat)±0.035(syst)  ps (corresponding to cτ(Λ0b)=420.1±13.7(stat)±10.6(syst)  μm, where c is the speed of light). The ratio of this result and the world average B0 lifetime yields τ(Λ0b)/τ(B0)=0.918±0.038 (stat) and (syst), in good agreement with recent theoretical predictions.