The difference in total widths between the B-c(+) and B+ mesons is measured using a data sample corresponding to an integrated luminosity of 3.0 fb(-1) collected by the LHCb experiment in 7 and 8 TeV centre-of-mass energy proton-proton collisions at the LHC. Through the study of the time evolution of B-c(+) -> J/psi pi(+) and B+ -> J/psi K+ decays, the width difference is measured to be Delta Gamma = Gamma(Bc+) - Gamma(Bc+) = 4.46 +/- 0.14 +/- 0.07 mm(-1) c, where the first uncertainty is statistical and the second systematic. The known lifetime of the B+ meson is used to convert this to a precise measurement of the B-c(+) clifetime, tau(Bc+) = 513.4 +/- 11.0 +/- 5.7 fs, where the first uncertainty is statistical and the second is systematic. (C) 2015 The Authors. Published by Elsevier B.V.