We present measurements of Collins asymmetries in the inclusive process e+e- --> pi pi €X, where pi stands for charged pions, at a center-of-mass energy of 10.6 GeV. We use a data sample of 468fb-1 collected by the BABAR experiment at the PEP-II B factory at SLAC, and consider pairs of charged pions produced in opposite hemispheres of hadronic events. We observe clear asymmetries in the distributions of the azimuthal angles in two distinct reference frames. We study the dependence of the asymmetry on several kinematic variables, finding that it increases with increasing pion momentum and momentum transverse to the analysis axis, and with increasing angle between the thrust and beam axis.