  We present novel spectropolarimetric observations of the hydrogen H$\alpha$
line taken with the Z\"urich Imaging Polarimeter (ZIMPOL) at the Gregory
Coud\'e Telescope of the Istituto Ricerche Solari Locarno (IRSOL). The linear
polarization is clearly dominated by the scattering of anisotropic radiation
and the Hanle effect, while the circular polarization by the Zeeman effect. The
observed linear polarization signals show a rich spatial variability, the
interpretation of which would open a new window for probing the solar
chromosphere. We study their spatial variation within coronal holes, finding a
different behaviour for the $U/I$ signals near the North and South solar poles.
We identify some spatial patterns, which may facilitate the interpretation of
the observations. In close-to-the-limb regions with sizable circular
polarization signals we find similar asymmetric $Q/I$ profiles. We also show
examples of net circular polarization profiles (NCP), along with the
corresponding linear polarization signals. The application of the weak field
approximation to the observed circular polarization signals gives $10\,$G
($40-60\,$G) in close to the limb quiet (plage) regions for the average
longitudinal field strength over the spatio-temporal resolution element.
