Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) ; Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) ; We describe a search for Z boson pair production in p(p)overbar collisions at root s=1.96 TeV with the D0 detector at the Fermilab Tevatron Collider using a data sample corresponding to an integrated luminosity of 2.7 fb(-1). Using the final state decay ZZ ->center dot(+)center dot(-)nu(nu)overbar (where center dot=e or mu) we find a signal with a 2.6 standard deviations significance (2.0 expected) corresponding to a cross section of sigma(p(p)overbar -> ZZ+X)=2.01 +/- 0.93(stat)+/- 0.29(sys) pb.