Abstract: A search for the rare decays B-S(0) -> tau(+) tau(-) and B-0 -> tau(+) tau(-) is performed using proton-proton collision data collected with the LHCb detector. The data sample corresponds to an integrated luminosity of 3 fb(-1) collected in 2011 and 2012. The tau leptons are reconstructed through the decay tau(-) -> pi(-) pi(+)pi(-) nu(tau). Assuming no contribution from B-S(0) -> tau(+) tau(-) decays, an upper limit is set on the branching fraction B(B-S(0) -> tau(+) tau(-)) < 6.8 x 10(-3) at the 95% confidence level. If instead no contribution from B-S(0) -> tau(+) tau(-) decays is assumed, the limit is B(B-s(0) -> tau(+) tau(-)) < 2.1 x 10(-3) at the 95% confidence level. These results correspond to the first direct limit on B(B-S(0) -> tau(+) tau(-)) and the world's best limit on B(B-S(0) -> tau(+) tau(-))