We describe a search for Z boson pair production in p¯ p collisions at √ 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 → ℓ + ℓ − ν ¯ ν (where ℓ = e or µ) we find a signal with a 2.6 standard deviations significance (2.0 expected) corresponding to a cross section of σ(p¯ p → ZZ + X) = 2.01 ± 0.93(stat.) ± 0.29(sys.) pb. 4 INTRODUCTION We report a search for Z boson pair production in p¯ p collisions in the mode where one Z boson decays into two charged leptons (either electrons or muons) and the other Z boson decays into two neutrinos (see Fig. 1). In the Standard Model (SM), ZZ production is the double gauge boson process with the lowest cross section and is the last remaining unobserved diboson process at the Tevatron, aside from the expected associated production of the Higgs boson. Observation of ZZ production therefore represents an essential step in Higgs boson searches in the ZH and W H channels with sensitivity at the level of the expected SM cross sections. Additionally, the ZZ process forms a background to Higgs boson searches, for example in the channels ZH → ℓ + ℓ − bb, ZH → ννbb and H → W + W − → ℓ + νℓ − ν. Unlike the W W and W Z processes, there are no expected SM contributions from triple gauge boson couplings involving two Z bosons and a measurement of the ZZ cross section represents a test for production of this final state via anomalous couplings. The process ZZ → ℓ + ℓ − ν ¯ ν has a branching ratio six times larger than that for the other purely leptonic process ZZ → ℓ + ℓ − ℓ ′+ ℓ ′−. After removing instrumental backgrounds, the dominant background in the ZZ → ℓ + ℓ − ν ¯ ν search arises from the process W W → ℓ + νℓ − ¯ ν, which produces the same final state particles. A kine-matic discriminant against background from W W → ℓ + νℓ − ¯ ν is employed. In contrast, a search in the ZZ → ℓ + ℓ − ℓ ′+ ℓ ′− channel benefits from having no significant …