We present a measurement of the cross section for Z boson production times the branching fraction to tau lepton pairs sigma(ppbar -> Z + X) Br(Z -> tau+ tau-) in proton-antiproton collisions at center of mass energy 1.96 TeV. The measurement is performed in the channel in which one tau lepton decays into a muon and neutrinos, and the other tau lepton decays hadronically or into an electron and neutrinos. The data sample corresponds to an integrated luminosity of 1.0 inverse fb collected with the D0 detector at the Fermilab Tevatron Collider. The sample contains 1511 candidate events with an estimated 20% background from jets or muons misidentified as tau leptons. We obtain sigma Br = 240 +/- 8 (stat) +/- 12 (sys) +/- 15 (lum) pb, which is consistent with the standard model prediction.