  A natural procedure is presented to measure the angle $\gamma$ from the decay
$B^{\pm} \to \pi^{\pm}\pi^+\pi^-$. 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 $\gamma$
could be measured with a combined error of the order of 20$^o$ with 90% of CL
after about a couple of years of running of the first generation of B
factories.
