A natural procedure is presented to measure the angle γ from the decay B^±→π^±π^+π^-. It is based in the Dalitz plot fitting analysis. Neither amplitudes nor strong phases have to be known a priori. We present simulations of this decay computing both statistical and theoretical uncertainties and analyze the experimental feasibility. We found that γ could be measured with a combined error of the order of 20^o with 90 after about a couple of years of running of the first generation of B factories.