First Evidence for the Decay<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>→</mml:mo><mml:msup><mml:mi>μ</mml:mi><mml:mo mathvariant="bold">+</mml:mo></mml:msup><mml:msup><mml:mi>μ</mml:mi><mml:mo mathvariant="bold">−</mml:mo></mml:msup></mml:math>

A search for the rare decays B(s)(0)→μ+ μ- and B(0)→μ+ μ- is performed with data collected in 2011 and 2012 with the LHCb experiment at the Large Hadron Collider. The data samples comprise 1.1 fb(-1) of proton-proton collisions at sqrt[s]=8 TeV and 1.0 fb(-1) at sqrt[s]=7 TeV. We observe an excess of B(s)(0)→μ+ μ- candidates with respect to the background expectation. The probability that the background could produce such an excess or larger is 5.3×10(-4) corresponding to a signal significance of 3.5 standard deviations. A maximum-likelihood fit gives a branching fraction of B(B(s)(0)→μ+ μ-)=(3.2(-1.2)(+1.5))×10(-9), where the statistical uncertainty is 95% of the total uncertainty. This result is in agreement with the standard model expectation. The observed number of B(0)→μ+ μ- candidates is consistent with the background expectation, giving an upper limit of B(B(0)→μ+ μ-)<9.4×10(-10) at 95% confidence level.