In this paper we present a precise measurement of the total ZZ production cross section in pp collisions at {surd}s= 1.96 TeV, using data collected with the CDF II detector corresponding to an integrated luminosity of approximately 6 fb-1. The result is obtained by combining separate measurements in the four-charged (llll), and two-charged-lepton and two-neutral-lepton (llvv) decay modes of the Z. The combined measured cross section for pp {to} ZZ is 1.64^(+0.44)_(-0.38) pb. This is the most precise measurement of the ZZ production cross section in 1.96 TeV pp collisions to date.