We report on the first calculation of next-to-next-to-leading order (NNLO) QCD corrections to the inclusive production of Z -boson pairs at hadron colliders. Numerical results are presented for pp collisions with centre-of-mass energy ( <math altimg="si1.gif" xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mi>s</mi></msqrt></math> ) ranging from 7 to 14 TeV. The NNLO corrections increase the NLO result by an amount varying from 11% to 17% as <math altimg="si1.gif" xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mi>s</mi></msqrt></math> goes from 7 to 14 TeV. The loop-induced gluon fusion contribution provides about <math altimg="si2.gif" xmlns="http://www.w3.org/1998/Math/MathML"><mn>60</mn><mtext>%</mtext></math> of the total NNLO ef...