Search for the Decays <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msubsup><mml:mi>B</mml:mi><mml:mi>s</mml:mi><mml:mn>0</mml:mn></mml:msubsup><mml:mo stretchy="false">→</mml:mo><mml:mrow><mml:msup><mml:mi>τ</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:msup><mml:mi>τ</mml:mi><mml:mo>−</mml:mo></mml:msup></mml:mrow></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>B</mml:mi><mml:mn>0</mml:mn></mml:msup><mml:mo stretchy="false">→</mml:mo><mml:mrow><mml:msup><mml:mi>τ</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:msup><mml:mi>τ</mml:mi><mml:mo>−</mml:mo></mml:msup></mml:mrow></mml:math>

A search for the rare decays B_{s}^{0}→τ^{+}τ^{-} and B^{0}→τ^{+}τ^{-} 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 τ leptons are reconstructed through the decay τ^{-}→π^{-}π^{+}π^{-}ν_{τ}. Assuming no contribution from B^{0}→τ^{+}τ^{-} decays, an upper limit is set on the branching fraction B(B_{s}^{0}→τ^{+}τ^{-})<6.8×10^{-3} at the 95% confidence level. If instead no contribution from B_{s}^{0}→τ^{+}τ^{-} decays is assumed, the limit is B(B^{0}→τ^{+}τ^{-})<2.1×10^{-3} at the 95% confidence level. These results correspond to the first direct limit on B(B_{s}^{0}→τ^{+}τ^{-}) and the world's best limit on B(B^{0}→τ^{+}τ^{-}).