We present an observation for ZZ -> l+l-l'+l'- (l, l' = e or mu) production in ppbar collisions at a center-of-mass energy of sqrt(s) = 1.96 TeV. Using 1.7 fb-1 of data collected by the D0 experiment at the Fermilab Tevatron Collider, we observe three candidate events with an expected background of 0.14 +0.03 -0.02 events. The significance of this observation is 5.3 standard deviations. The combination of D0 results in this channel, as well as in ZZ -> l+l-nunubar, yields a significance of 5.7 standard deviations and a combined cross section of sigma(ZZ) = 1.60 +/- 0.63 (stat.) +0.16 -0.17 (syst.) pb.