Abstract: We report a measurement of the mass difference between neutral charm-meson eigenstates using a novel approach that enhances sensitivity to this parameter. We use 2.3 x 10(6) D-0 -> K-S(0)pi(+)pi(-) decays reconstructed in proton-proton collisions collected by the LHCb experiment in 2011 and 2012. Allowing for CP violation in mixing and in the interference between mixing and decay, we measure the CP-averaged normalized mass difference x(cp)= [2.7 +/- 1.6(stat) +/- 0.4(syst)] x 10(-3) and the CP-violating parameter Delta x = [-0.53 +/- 0.70(stat) +/- 0.22(syst)] x 10(-3). The results are consistent with CP symmetry. These determinations are the most precise from a single experiment and, combined with current world-average results, yield the fast evidence that the masses of the neutral charm-meson eigenstates differ.