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 $5times 10^{10}~rm M_odot$ 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.
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