  The inelastic hadronic cross section in proton-lead collisions at a
centre-of-mass energy per nucleon pair of 5.02 TeV is measured with the CMS
detector at the LHC. The data sample, corresponding to an integrated luminosity
of 12.6 +/- 0.4 inverse nanobarns, has been collected with an unbiased trigger
for inclusive particle production. The cross section is obtained from the
measured number of proton-lead collisions with hadronic activity produced in
the pseudorapidity ranges 3 < eta < 5 and/or -5 < eta < -3, corrected for
photon-induced contributions, experimental acceptance, and other instrumental
effects. The inelastic cross section is measured to be sigma[inel,pPb] = 2061
+/- 3 (stat) +/- 34 (syst) +/- 72 (lum) mb. Various Monte Carlo generators,
commonly used in heavy ion and cosmic ray physics, are found to reproduce the
data within uncertainties. The value of sigma[inel,pPb] is compatible with that
expected from the proton-proton cross section at 5.02 TeV scaled up within a
simple Glauber approach to account for multiple scatterings in the lead
nucleus, indicating that further net nuclear corrections are small.
