We report measurements of the lifetimes of the Lambda(+)(c), Xi(+)(c) and Xi(0)(c) charm baryons using proton- proton collision data at center- of- mass energies of 7 and 8 TeV, corresponding to an integrated luminosity of 3.0 fb(-1), collected by the LHCb experiment. The charm baryons are reconstructed through the decays Lambda(+)(c) -> pK(-)pi(+),. Xi(+)(c) -> pK(-) pi(+) and Xi(0)(c) -> pK(-) K- pi(+), and originate from semimuonic decays of beauty baryons. The lifetimes are measured relative to that of the D+ meson, and are determined to be tau Lambda(+)(c) = 203.5 +/- 1.0 +/- 1.3 +/- 1.4 fs; tau Xi(+)(c) = 456.8 +/- 3.5 +/- 2.9 +/- 3.1 fs; tau Xi(0)(c) = 154.5 +/- 1.7 +/- 1.6 +/- 1.0 fs; where the uncertainties are statistical, systematic, and due to the uncertainty in the D+ lifetime. The measurements are approximately 3- 4 times more precise than the current world average values. The. +c and Xi(+)(c) lifetimes are in agreement with previous measurements; however, the Xi(0)(c) baryon lifetime is approximately 3.3 standard deviations larger than the world average value.