Using a proton-proton collision data sample corresponding to an integrated luminosity of 3     fb − 1 collected by LHCb at center-of-mass energies of 7 and 8 TeV, about 3800 Ξ 0 b → Ξ + c π − , Ξ + c → p K − π + signal decays are reconstructed. From this sample, the first measurement of the Ξ 0 b baryon lifetime is made, relative to that of the Λ 0 b baryon. The mass differences M ( Ξ 0 b ) − M ( Λ 0 b ) and M ( Ξ + c ) − M ( Λ + c ) are also measured with precision more than 4 times better than the current world averages. The resulting values are τ Ξ 0 b τ Λ 0 b = 1.006 ± 0.018 ± 0.010 , M ( Ξ 0 b ) − M ( Λ 0 b ) = 172.44 ± 0.39 ± 0.17     MeV / c 2 , M ( Ξ + c ) − M ( Λ + c ) = 181.51 ± 0.14 ± 0.10     MeV / c 2 , where the first uncertainty is statistical and the second is systematic. The relative rate of Ξ 0 b to Λ 0 b baryon production is measured to be f Ξ 0 b f Λ 0 b B ( Ξ 0 b → Ξ + c π − ) B ( Λ 0 b → Λ + c π − ) B ( Ξ + c → p K − π + ) B ( Λ + c → p K − π + ) = ( 1.88 ± 0.04 ± 0.03 ) × 1 0 − 2 , where the first factor is the ratio of fragmentation fractions, b → Ξ 0 b relative to b → Λ 0 b . Relative production rates as functions of transverse momentum and pseudorapidity are also presented.