  A search for the rare decays $B^0_s \to\mu^+\mu^-$ and $B^0 \to\mu^+\mu^-$ is
performed at the LHCb experiment. The data analysed correspond to an integrated
luminosity of 1 fb$^{-1}$ of $pp$ collisions at a centre-of-mass energy of 7
TeV and 2 fb$^{-1}$ at 8 TeV. An excess of $B^0_s \to\mu^+\mu^-$ signal
candidates with respect to the background expectation is seen with a
significance of 4.0 standard deviations. A time-integrated branching fraction
of ${\cal B}(B^0_s \to\mu^+\mu^-) = (2.9^{+1.1}_{-1.0})\times 10^{-9}$ is
obtained and an upper limit of ${\cal B}(B^0 \to\mu^+\mu^-) < 7.4\times
10^{-10}$ at 95% confidence level is set. These results are consistent with the
Standard Model expectations.
