In this paper, we study the heating of the magnetized solar chromosphere induced by the large fraction of neutral atoms present in this layer. The presence of neutrals, together with the decrease with height of the collisional coupling, leads to deviations from the classical magnetohydrodynamic behavior of the chromospheric plasma. A relative net motion appears between the neutral and ionized components, usually referred to as ambipolar diffusion. The dissipation of currents in the chromosphere is enhanced by orders of magnitude due to the action of ambipolar diffusion, as compared with the standard ohmic diffusion. We propose that a significant amount of magnetic energy can be released to the chromosphere just by existing force-free 10-40 G magnetic fields there. As a consequence, we conclude that ambipolar diffusion is an important process that should be included in chromospheric heating models, as it has the potential to rapidly heat the chromosphere. We perform analytical estimations and numerical simulations to prove this idea.