A discovery of the rare decay B+ -> pi(+)mu(+)mu(-) is presented. This decay is observed for the first time, with 5.2 sigma significance. The observation is made using p p collision data, corresponding to an integrated luminosity of 1.0 fb(-1), collected with the LHCb detector. The measured branching fraction is (2.3 +/- 0.6 (stat.) +/- 0.1 (syst.)) x 10(-8), and the ratio of the B+ -> pi(+)mu(+)mu(-) and B+ -> K+mu(+)mu(-) branching fractions is measured to be 0.053 +/- 0.014 (stat.) +/- 0.001 (syst.).