A measurement is presented of the neutron production rate in lead by high energy cosmic-ray muons at a depth of 2850 m water equivalent (w.e.) and a mean muon energy of 260 GeV. The measurement exploits the delayed coincidences between muons and the radiative capture of induced neutrons in a highly segmented tonne scale plastic scintillator detector. Detailed Monte Carlo simulations reproduce well the measured capture times and multiplicities and, within the dynamic range of the instrumentation, the spectrum of energy deposits. By comparing measurements with simulations of neutron capture rates a neutron yield in lead of (5.78^{+0.21}_{-0.28}) x 10^{-3} neutrons/muon/(g/cm^{2}) has been obtained. Absolute agreement between simulation and data is of order 25%. Consequences for deep underground rare event searches are discussed.
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