A search for the rare leptonic decay B +. mu + mu - mu +.mu is performed using proton- proton collision data corresponding to an integrated luminosity of 4.7 fb - 1 collected by the LHCb experiment. The search is carried out in the region where the lowest of the two mu + mu - mass combinations is below 980 MeV/ c2. The data are consistent with the background- only hypothesis and an upper limit of 1.6x10 - 8 at 95% confidence level is set on the branching fraction in the stated kinematic region.