  We present Very Long Baseline Array (VLBA) HI absorption observations of the
core region of the powerful radio galaxy Cygnus A. These data show both broad
(FWHM = 231 \pm 21 km/s) and narrow (FWHM <30 km/s) velocity width absorption
components. The broad velocity absorption shows high opacity on the counter
jet, low opacity against the core and no absorption on the jet side. We argue
that these results are most naturally explained by a circumnuclear HI absorbing
disk orientated roughly perpendicular to the jet axis. We estimate that the HI
absorbing gas lies at a radius of ~80 pc has a scale height of about 20 pc,
density n > 10^{4} cm^{-3} and total column density in the range
10^{23}-10^{24} cm^{-2}. Models in which the HI absorption is primarily from an
atomic or a molecular gas phase can both fit our data. Modelling taking into
account the effective beam shows that the broad HI absorbing gas component does
not cover the radio core in Cygnus A and therefore does not contribute to the
gas column that blocks our view of the hidden quasar nucleus. If however Cygnus
A were observed from a different direction, disk gas on ~100 pc radius scales
would contribute significantly to the nuclear column density, implying that in
some radio galaxies gas on these scales may contribute to the obscuration of
the central engine. We argue that the circumnuclear torus in Cygnus A contains
too little mass to power the AGN over > 10^{7} yr but that material in the
outer HI absorbing gas disk can provide a reservoir to fuel the AGN and
replenish torus clouds. The second narrow HI absorption component is
significantly redshifted (by 186km/s) with respect to the systemic velocity and
probably traces infalling gas which will ultimately fuel the source. [abridged]
