  The first measurement of neutron emission in electromagnetic dissociation of
$^{208}$Pb nuclei at the LHC is presented. The measurement is performed using
the neutron Zero Degree Calorimeters of the ALICE experiment, which detect
neutral particles close to beam rapidity. The measured cross sections of single
and mutual electromagnetic dissociation of Pb nuclei at $\sqrt{s_{\rm NN}}$ =
2.76 TeV with neutron emission are $\sigma_{\rm single\ EMD} = 187.4\pm0.2$
(stat.) $^{+13.2} _{-11.2}$ (syst.) b and $\sigma_{\rm mutual\ EMD} =
5.7\pm0.1$ (stat.) $\pm$0.4 (syst.) b, respectively. The experimental results
are compared to the predictions from a relativistic electromagnetic
dissociation model.
