  We present the discovery of a 4 kpc molecular gas lane in the Cygnus A host
galaxy, using ALMA CO 2-1 observations. The gas lane is oriented roughly
perpendicular to the projected radio jet axis. The CO emission generally
follows the clumpy dust lanes seen in HST I-band images. The total molecular
gas mass is $30\times 10^8$ M$_\odot$ for Milky Way type clouds, and $3.6
\times 10^8$ M$_\odot$ for starburst conditions. There is a velocity change
from the northern to southern CO peaks of about $\pm 175$~km~s$^{-1}$, and an
apparently smooth velocity gradient between the peaks, although the emission in
the central region is weak. In the inner $\sim 0.5"$ projected distance from
the radio core, comparison of the CO velocities to those observed for H$_2$
2.1218 $\mu$m emission shows higher velocities for the vibrationally excited
warm molecular gas than the cooler CO 2-1 line emitting gas at similar
projected radii. A possible explanation for these different projected
velocities at a given radius is that the cooler CO gas is distributed in a
clumpy ring at radius $\sim 1.5"$ to $2"$, while the warm H$_2$ 2.12$\mu$m
emitting gas is interior to this ring. Of course, the current data cannot
rule-out a clumpy, amorphous molecular gas distribution linearly distributed
perpendicular to the radio jet axis. We consider surface brightness properties
on scales down to $\sim 265$~pc, and discuss the Cygnus A results in the
context of other radio galaxies with CO emission.
