We report measurements of the lifetimes of the , and charm baryons using proton-proton collision data at center-of-mass energies of 7 and 8 TeV, corresponding to an integrated luminosity of , collected by the LHCb experiment. The charm baryons are reconstructed through the decays , and , and originate from semimuonic decays of beauty baryons. The lifetimes are measured relative to that of the meson, and are determined to be τΛc+=203.5±1.0±1.3±1.4  fs,  τΞc+=456.8±3.5±2.9±3.1  fs,  τΞc0=154.5±1.7±1.6±1.0  fs, where the uncertainties are statistical, systematic, and due to the uncertainty in the lifetime. The measurements are approximately 3–4 times more precise than the current world average values. The and lifetimes are in agreement with previous measurements; however, the baryon lifetime is approximately 3.3 standard deviations larger than the world average value.