The first measurement of inclusive Z > tau(+) tau(-) production in pp collisions at the LHC is presented, in the final states mu+hadrons, e+hadrons, e-mu, and mu+mu. The data sample corresponds to an integrated luminosity of 36 pb(-1) collected with the CMS detector. The measured cross section is sigma (pp -> ZX) x B (Z -> tau(+)tau(-)) = 1.00 +/- 0.05 (stat.)+/- 0.08 (syst.) +/- 0.04 (lumi.) nb, which is in good agreement with the next-to-next-to-leading order QCD prediction and improves on previous measurements in the Z -> e(+)e(-) and mu(+)mu(-) channels. The reconstruction efficiency for hadronic T decays is determined with a precision of 7%.