  We present new high resolution (100 arcsec) neutral hydrogen (H I)
self-absorption images of the Riegel-Crutcher cloud obtained with the Australia
Telescope Compact Array and the Parkes Radio Telescope. The Riegel-Crutcher
cloud lies in the direction of the Galactic center at a distance of 125 +/- 25
pc. Our observations resolve the very large, nearby sheet of cold hydrogen into
a spectacular network of dozens of hair-like filaments. Individual filaments
are remarkably elongated, being up to 17 pc long with widths of less than ~0.1
pc. The strands are reasonably cold, with spin temperatures of 40 K and in many
places appearing to have optical depths larger than one. Comparing the H I
images with observations of stellar polarization we show that the filaments are
very well aligned with the ambient magnetic field. We argue that the structure
of the cloud has been determined by its magnetic field. In order for the cloud
to be magnetically dominated the magnetic field strength must be > 30
microGauss.
