  We compute the next-to-leading order QCD corrections to the production of two
Z-bosons in the annihilation of two gluons at the LHC. Being enhanced by a
large gluon flux, these corrections provide distinct and, potentially, the
dominant part of the N$^3$LO QCD contributions to Z-pair production in proton
collisions. The $gg \to ZZ$ annihilation is a loop-induced process that
receives the dominant contribution from loops of five light quarks, that are
included in our computation in the massless approximation. We find that QCD
corrections increase the $gg \to ZZ$ production cross section by ${\cal
O}(50\%-100\%)$ depending on the values of the renormalization and
factorization scales used in the leading order computation, and the collider
energy. The large corrections to $gg \to ZZ$ channel increase the $pp \to ZZ$
cross section by about six to eight percent, exceeding the estimated
theoretical uncertainty of the recent NNLO QCD calculation.
