  The commensurate charge density wave (CDW) in the layered compound
$1T$-TaS$_2$ has hitherto mostly been treated as a quasi two-dimensional
phenomenon. Recent band structure calculations have, however, predicted that
the CDW coexists with a nearly one-dimensional metallic dispersion
perpendicular to the crystal planes. Using synchrotron radiation based
angle-resolved photoemission spectroscopy, we show that this metallic band does
in fact exist. Its occupied band width is in excellent agreement with
predictions for a simple $\tau_c$ stacking order of the CDW between adjacent
layers and its periodicity in the $c$ direction is $2 \pi / c$.
