The Hanle effect in strong spectral lines is the physical mechanism that should be increasingly exploited for quantitative explorations of the magnetism of the quiet solar chromospheric plasma. Here we show, by means of multilevel radiative transfer calculations and new spectropolarimetric observations, that the amplitude and shape of the scattering polarization profiles of the Hα line is very sensitive to the strength and structure of the chromospheric magnetic field. The interpretation of the observations in terms of one-dimensional radiative transfer modeling suggests that there is an abrupt magnetization in the upper chromosphere of the quiet Sun.