  Active galactic nuclei play a crucial role in the accretion and ejection of
gas in galaxies. Although their outflows are well studied, finding direct
evidence of accretion has proved very difficult and has so far been done for
very few sources. A promising way to study the significance of cold accretion
is by observing the absorption of an active galactic nucleus's extremely bright
radio emission by the cold gas lying along the line-of-sight. As such, we
present ALMA CO(1-0) and CO(2-1) observations of the Hydra-A brightest cluster
galaxy (z=0.054) which reveal the existence of cold, molecular gas clouds along
the line-of-sight to the galaxy's extremely bright and compact mm-continuum
source. They have apparent motions relative to the central supermassive black
hole of between -43 and -4 km s$^{-1}$ and are most likely moving along stable,
low ellipticity orbits. The identified clouds form part of a $\sim$$10^{9}$
$\text{M}_{\odot}$, approximately edge-on disc of cold molecular gas. With peak
CO(2-1) optical depths of $\tau$=0.88 $^{+0.06}_{-0.06}$, they include the
narrowest and by far the deepest absorption of this type which has been
observed to date in a brightest cluster galaxy. By comparing the relative
strengths of the lines for the most strongly absorbing region, we are able to
estimate a gas temperature of $42^{+25}_{-11}$ K and line-of-sight column
densities of $N_{CO}=2^{+3}_{-1}\times 10 ^{17} cm^{-2}$ and $N_{ H_{2}
}=7^{+10}_{-4}\times 10 ^{20} cm^{-2}$.
