  There is a thin transition region (TR) in the solar atmosphere where the
temperature rises from 10,000 K in the chromosphere to millions of degrees in
the corona. Little is known about the mechanisms that dominate this enigmatic
region other than the magnetic field plays a key role. The magnetism of the TR
can only be detected by polarimetric measurements of a few ultraviolet (UV)
spectral lines, the Lyman-$\alpha$ line of neutral hydrogen at 121.6 nm (the
strongest line of the solar UV spectrum) being of particular interest given its
sensitivity to the Hanle effect (the magnetic-field-induced modification of the
scattering line polarization). We report the discovery of linear polarization
produced by scattering processes in the Lyman-$\alpha$ line, obtained with the
Chromospheric Lyman-Alpha Spectro-Polarimeter (CLASP) rocket experiment. The
Stokes profiles observed by CLASP in quiet regions of the solar disk show that
the $Q/I$ and $U/I$ linear polarization signals are of the order of 0.1 % in
the line core and up to a few percent in the nearby wings, and that both have
conspicuous spatial variations with scales of $\sim 10$ arcsec. These
observations help constrain theoretical models of the chromosphere-corona TR
and extrapolations of the magnetic field from photospheric magnetograms. In
fact, the observed spatial variation from disk to limb of polarization at the
line core and wings already challenge the predictions from three-dimensional
magnetohydrodynamical models of the upper solar chromosphere.
