  We report on the first measurement of an excess in the yield of J/$\psi$ at
very low transverse momentum ($p_{\rm T}< 0.3$ GeV/$c$) in peripheral hadronic
Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV, performed by ALICE at the
CERN LHC. Remarkably, the measured nuclear modification factor of J/$\psi$ in
the rapidity range $2.5<y<4$ reaches about 7 (2) in the $p_{\rm T}$ range 0-0.3
GeV/$c$ in the 70-90% (50-70%) centrality class. The J/$\psi$ production cross
section associated with the observed excess is obtained under the hypothesis
that coherent photoproduction of J/$\psi$ is the underlying physics mechanism.
If confirmed, the observation of J/$\psi$ coherent photoproduction in Pb-Pb
collisions at impact parameters smaller than twice the nuclear radius opens new
theoretical and experimental challenges and opportunities. In particular,
coherent photoproduction accompanying hadronic collisions may provide insight
into the dynamics of photoproduction and nuclear reactions, as well as become a
novel probe of the Quark-Gluon Plasma.
