We present detailed electron-spin resonance investigations on single crystals of the one-dimensional vanadium-oxide bronze beta-Na(1/3)V2O5. From the angular dependence of the g value it can be concluded that the electrons are primarily located on the V1 zigzag chains. The anisotropy of the linewidth, which is determined by the intrachain symmetric anisotropic exchange interaction, favors statistic electron distribution in the metallic and blockwise charge-order in the insulating phase. The temperature dependence of the linewidth indicates the opening of a charge gap at the metal-to-insulator transition at T(MI)=132 K.