  The production of same-sign W-boson pairs from double parton scatterings
(DPS) in proton-lead (p-Pb) collisions at the CERN Large Hadron Collider is
studied. The signal and background cross sections are estimated with
next-to-leading-order perturbative QCD calculations using nuclear parton
distribution functions for the Pb ion. At sqrt(sNN) = 8.8 TeV the cross section
for the DPS process is about 150 pb, i.e. 600 times larger than that in
proton-proton collisions at the same centre-of-mass energy and 1.5 times higher
than the pPb --> WW+2-jets single-parton background. The measurement of such a
process, where 10 events with fully leptonic W's decays are expected after cuts
in 2 pb^{-1}, would constitute an unambiguous DPS signal and would help
determine the effective sigma_eff parameter characterising the transverse
distribution of partons in the proton.
