We calculate nuclear shadowing in lepton-deuteron deep inelastic scattering, which arises from the double scattering of the virtual photon from both nucleons in the deuteron. The total correction to the deuteron structure function is found to be less than about 1\% at small Bjorken-x, but dependent on the model deuteron wavefunction. The resulting increase in the corrected neutron structure function is between 1-2\% for x near 0.004, which leads to a 4-10\% decrease in the value of the Gottfried sum obtained recently by the New Muon Collaboration.

20 pages (figures available upon request), (to appear in Phys.Rev.D) ADP-92-192/T120