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We report measurements of the lifetimes of the Λ+c, Ξ+c and Ξ0c 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 Λ+c→pK−π+, Ξ+c→pK−π+ and Ξ0c→pK−K−π+, and originate from semimuonic decays of beauty baryons. The lifetimes are measured relative to that of the D+ meson, and are determined to be τΛ+c=203.5±1.0±1.3±1.4  fs,  τΞ+c=456.8±3.5±2.9±3.1  fs,  τΞ0c=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 Λ+c and Ξ+c lifetimes are in agreement with previous measurements; however, the Ξ0c baryon lifetime is approximately 3.3 standard deviations larger than the world average value.