  Routine ultraviolet imaging of the Sun's upper atmosphere shows the
spectacular manifestation of solar activity; yet we remain blind to its main
driver, the magnetic field. Here we report unprecedented spectropolarimetric
observations of an active region plage and its surrounding enhanced network,
showing circular polarization in ultraviolet (Mg II $h$ & $k$ and Mn I) and
visible (Fe I) lines. We infer the longitudinal magnetic field from the
photosphere to the very upper chromosphere. At the top of the plage
chromosphere the field strengths reach more than 300 gauss, strongly correlated
with the Mg II $k$ line core intensity and the electron pressure. This unique
mapping shows how the magnetic field couples the different atmospheric layers
and reveals the magnetic origin of the heating in the plage chromosphere.
