  We report ALMA Early Science observations of the Abell 1835 brightest cluster
galaxy (BCG) in the CO (3-2) and CO (1-0) emission lines. We detect $5\times
10^{10}~\rm M_\odot$ of molecular gas within 10 kpc of the BCG. Its ensemble
velocity profile width of $\sim 130 ~\rm km~s^{-1}$ FWHM is too narrow for the
molecular cloud sto be supported in the galaxy by dynamic pressure. The gas may
instead be supported in a rotating, turbulent disk oriented nearly face-on.
Roughly $10^{10}~\rm M_\odot$ of molecular gas is projected $3-10 ~\rm kpc$ to
the north-west and to the east of the nucleus with line of sight velocities
lying between $-250 ~\rm km~s^{-1}$ to $+480 ~\rm km~s^{-1}$ with respect to
the systemic velocity. The high velocity gas may be either inflowing or
outflowing. However, the absence of high velocity gas toward the nucleus that
would be expected in a steady inflow, and its bipolar distribution on either
side of the nucleus, are more naturally explained as outflow. Star formation
and radiation from the AGN are both incapable of driving an outflow of this
magnitude. If so, the molecular outflow may be associated a hot outflow on
larger scales reported by Kirkpatrick and colleagues. The molecular gas flow
rate of approximately $200~\rm M_\odot ~yr^{-1}$ is comparable to the star
formation rate of $100-180~\rm M_\odot ~yr^{-1}$ in the central disk. How radio
bubbles would lift dense molecular gas in their updrafts, how much gas will be
lost to the BCG, and how much will return to fuel future star formation and AGN
activity are poorly understood. Our results imply that radio-mechanical (radio
mode) feedback not only heats hot atmospheres surrounding elliptical galaxies
and BCGs, it is able to sweep higher density molecular gas away from their
centers.
