Magnetic fields play a key role in most astrophysical systems, from the Sun to active galactic nuclei. They can be studied through their effects on atomic energy levels, which produce polarized spectral lines. In particular, anisotropic radiation `pumping' processes (which send electrons to higher atomic levels) induce population imbalances that are modified by weak magnetic fields. Here we report peculiarly polarized light in the HeI 10,830-Å multiplet observed in a coronal filament located at the centre of the solar disk. We show that the polarized light arises from selective absorption from the ground level of the triplet system of helium, and that it implies the presence of magnetic fields of the order of a few gauss that are highly inclined with respect to the solar radius vector. This disproves the common belief that population imbalances in long-lived atomic levels are insignificant in the presence of inclined fields of the order of a few gauss, and opens up a new diagnostic window for the investigation of solar magnetic fields.