  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
Bay's liquid scintillator is measured to be $Y_n=(10.26\pm 0.86)\times
10^{-5}$, $(10.22\pm 0.87)\times 10^{-5}$, and $(17.03\pm 1.22)\times
10^{-5}~\mu^{-1}~$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.
