  We show that the recent ALICE measurements of exclusive J/{\psi} production
in ultraperipheral PbPb collisions at 2.76 TeV provide the first direct
experimental evidence for the strong nuclear gluon shadowing in lead at $x \sim
10^{-3}$. The evidence is based on the comparison of the nuclear suppression
factor S(x\approx 0.001)=0.61^{+0.05}_{-0.04} found in the analysis of the
coherent J/{\psi} photoproduction cross sections measured by ALICE with the
nuclear gluon shadowing predicted by the global fits of nuclear parton
distributions and by the leading twist theory of nuclear shadowing.
