  We consider QCD radiative corrections to the production of four charged
leptons in the ZZ signal region at the LHC. We report on the complete
calculation of the next-to-next-to-leading order (NNLO) corrections to this
process in QCD perturbation theory. Numerical results are presented for
$\sqrt{s}=8$ TeV, using typical selection cuts applied by the ATLAS and CMS
collaborations. The NNLO corrections increase the NLO fiducial cross section by
about $15\%$, and they have a relatively small impact on the shape of the
considered kinematical distributions. In the case of the $\Delta\Phi$
distribution of the two Z candidates, the NNLO corrections improve the
agreement of the theoretical prediction with the CMS data.
