We report on a detailed radiative transfer modeling of the observed scattering polarization in the H-alpha line, which allows us to infer quantitative information on the magnetization of the quiet solar chromosphere. Our analysis suggests the presence of a magnetic complexity zone with a mean field strength B > 30 G lying just below the sudden transition region to the coronal temperatures. The chromospheric plasma directly underneath is very weakly magnetized, with B ~ 1 G. The possible existence of this abrupt change in the degree of magnetization of the upper chromosphere of the quiet Sun might have large significance for our understanding of chromospheric (and, therefore, coronal) heating.