A particularly interesting line for exploring the physical conditions of the quiet solar chromosphere is Halpha , but its intensity profile is magnetically insensitive and the small circular polarization signatures produced by the longitudinal Zeeman effect come mainly from the underlying photosphere. Here we show that the Hanle effect in Halpha provides quantitative information on the magnetism of the quiet chromosphere. To this end, we calculate the response function of the emergent scattering polarization to perturbations in the magnetic field.