  We present ALMA CO(1-0) and CO(3-2) observations of the brightest cluster
galaxy (BCG) in the 2A 0335+096 galaxy cluster (z = 0.0346). The total
molecular gas mass of (1.13+/-0.15) x 10^9 M_sun is divided into two
components: a nuclear region and a 7 kpc long dusty filament. The central
molecular gas component accounts for (3.2+/-0.4) x 10^8 M_sun of the total
supply of cold gas. Instead of forming a rotationally-supported ring or disk,
it is composed of two distinct, blueshifted clumps south of the nucleus and a
series of low-significance redshifted clumps extending toward a nearby
companion galaxy. The velocity of the redshifted clouds increases with radius
to a value consistent with the companion galaxy, suggesting that an interaction
between these galaxies <20 Myr ago disrupted a pre-existing molecular gas
reservoir within the BCG. Most of the molecular gas, (7.8+/-0.9) x 10^8 M_sun,
is located in the filament. The CO emission is co-spatial with a 10^4 K
emission-line nebula and soft X-rays from 0.5 keV gas, indicating that the
molecular gas has cooled out of the intracluster medium over a period of 25-100
Myr. The filament trails an X-ray cavity, suggesting that the gas has cooled
from low entropy gas that has been lifted out of the cluster core and become
thermally unstable. We are unable to distinguish between inflow and outflow
along the filament with the present data. Cloud velocities along the filament
are consistent with gravitational free-fall near the plane of the sky, although
their increasing blueshifts with radius are consistent with outflow.
