Neutrons produced by cosmic ray muons are an important background for underground experiments studying neutrino oscillations, neutrinoless double beta decay, dark matter, and other rare-event signals. A measurement of the neutron yield in the three different experimental halls of the Daya Bay Reactor Neutrino Experiment at varying depth is reported. The neutron yield in Daya Bays liquid scintillator is measured to be $Y_n=(10.26pm 0.86)times 10^{-5}$, $(10.22pm 0.87)times 10^{-5}$, and $(17.03pm 1.22)times 10^{-5}~mu^{-1}~$g$^{-1}~$cm$^2$ at depths of 250, 265, and 860 meters-water-equivalent. These results are compared to other measurements and the simulated neutron yield in Fluka and Geant4. A global fit including the Daya Bay measurements yields a power law coefficient of $0.77 pm 0.03$ for the dependence of the neutron yield on muon energy.
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