The top quark pair production cross section is measured in dilepton events with one electron or muon, and one hadronically decaying tau lepton from the decay t anti-t to (l nu(l)) (tau nu(tau)) b anti-b, where l can be either an electron or a muon. The data sample corresponds to an integrated luminosity of 2.0 inverse femtobarns for the electron channel and 2.2 inverse femtobarns for the muon channel, collected by the CMS detector at the LHC. This is the first measurement of the t anti-t cross section explicitly including tau leptons in proton-proton collisions at sqrt(s) = 7 TeV. The measured value sigma(t anti-t) = 143 +/- 14 (stat.) +/- 22 (syst.) +/- 3 (lumi.) pb is consistent with the standard model predictions.